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Certified General Accountants of British Columbia
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FINANCIAL ACCOUNTING ASSETS - FA2
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MODULE 5, INTEREST CONCEPTS OF FUTURE & PRESENT VALUES
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MS. DALLAS:
Welcome to the CGA Financial Accounting
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Assets, module 5, Interest concepts of future &
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present value, presented by Laura Dallas and
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Erin Creagh.
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FA2, MODULE 5, PART 1, INTRODUCTION
You are now listening to Module 5, part 1,
the introduction.
There will be five parts to this lecture.
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Part 2, is the Module Summary and Learning
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Objective; Part 3, Past Exam Analysis; Part 4,
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the Overview and Definitions Topics 5.1 – 5.2,
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and Part 5, will be topic 5.3 to 5.5.
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topic 5.6 is a computer illustration and you
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will be doing that part on your own.
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Note that
So welcome to interest calculations.
This
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module will be one that either you love, because
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you already know how to do it, or it can be your
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worst nightmare if you haven’t worked with
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interest and financial calculators before.
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A quick overview of the module 5 topics
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are: the time value of money; basic interest
Copyright © The Certified General Accountants Association of British Columbia. All rights reserved.
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concepts; computing present and future values;
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periodic payments required for present value and
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future value problems; topic 5, computing the
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terms; and topic 6, the computer illustration.
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There is not one specific calculator that
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students can use.
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calculator they want, so trying to teach each
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student how to use their financial calculator
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and automatically getting the correct answer,
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can be a challenge in this format.
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purchase a financial calculator that you feel
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comfortable with, but make sure you know you
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really need a financial calculator and not a
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scientific calculator.
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after you finish this module you will certainly
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know why.
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Students can use any
You can
Big differences and
At the CGA website, you will find a heading
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“Allowable Examination Room Materials and
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Calculators”.
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of print screen what the window looks like, what
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you now want to go and find if you want to
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double check what I am going to tell you here.
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But basically students may use their own
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calculator in examinations, provided they meet
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the following guidelines: the calculator is
I have cut and pasted here a sort
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silent, battery operated and non-printing; the
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calculator has only one line of display, and the
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calculator does not have alpha keys.
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keys allowing text entry.
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important.
That means
That is very
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Students are responsible for ensuring that
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the calculator batteries are fully operational.
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There will be no exchange or borrowing of
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calculators or batteries during the exam.
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no operating instructions allowed in the exam
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room either.
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other type of aid or material is permitted in
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the exam room.
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And
No other mechanical, electronic or
You can bring in spare batteries just as
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you can bring in spare pencils and spare
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erasers.
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in spare batteries for you calculator.
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have seen some students bring in two calculators
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one that’s their financial calculator for doing
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all financial information, and sometime students
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will bring in a calculator that has big key pad
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numbers so they can quickly add something up if
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necessary.
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calculators but they all must follow those rules
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about being silent and non-printing et cetera,
If you feel the need to you can bring
And I
So, yes, you can have two
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et cetera.
So hopefully you hear me quite clearly that
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I do highly recommend that you have financial
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calculator.
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calculate the present value and the future value
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and the amounts.
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calculate it all if you know all the formulas
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and things like that but an investment in a good
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financial calculator will be an asset to you in
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further CGA courses, including the finance
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courses.
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calculator can be an accountant’s best friend.
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So get one that you like and that you can use
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well and feel confident using it well.
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You’ll be able to automatically
Yes, you can manually
But truthfully a good financial
And of course remember that it is your
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responsibility to know how to use your
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calculator, and be prepared for the exam.
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students that know how to use it and calculate
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the present values and things like that quickly
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just -- you don’t have to spend time double
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guessing yourself, it’s something you just want
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to know.
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for future courses.
The
And like I say it is in preparation
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In this module, the solutions to the
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numerical calculations are demonstrated using
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the most common format of data entry for
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financial calculators.
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could be slightly different across different
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brands and models of calculators.
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look at your owner’s manual for some specific
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instructions.
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are almost like car manuals they’re pretty
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detailed and pretty long.
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meaning to scare you about these financial
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calculators, but if you know how to use it
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definitely a great asset for this exam.
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But the method of input
So you can
Although those owner’s manuals
So I am certainly not
Now some students who encounter little
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difficulty with interest and present value
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concepts, the reason they don’t encounter
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difficulties, is most likely because they have
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taken a business math course, usually at a
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college level or they have taken a finance
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course.
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course at a college level and found that the
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successful students are the ones that know how
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to use their calculators.
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just memorize all the formulas but you can’t
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keep those with you forever.
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students that get A’s are the ones that know how
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to use their calculators.
And I have taught the business math
Some students like to
Honestly the
And some of you are
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saying, “How difficult is it?”
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saying for adding and subtracting I’m saying I
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want you to know how to use it to calculate the
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present value.
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I am not just
And also if you need a refresher, there are
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many business math textbooks out there.
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see them at your local college bookstore, or
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even at your library.
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same sort of website as the FA2 text.
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in from McGraw Hill and college and you will
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find a list of quite a few textbooks listed
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there, and you will see certainly business math
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textbooks there.
You can
Or you can just use the
Just type
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If you do end up at that McGraw Hill
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website usually the first one you might see is
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the one called Business Mathematics in Canada,
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by Ernest Jerome.
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I quite like it.
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publisher McGraw Hill is that the text websites
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are all set out in a similar fashion.
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you use the text for the FA2 website, you will
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certainly be able to use up these business math
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tips from this website equally as well.
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might quite enjoy that.
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if you can find that.
I have used that text before,
And the nice thing about the
So, if
And you
So have a look and see
So you certainly don’t
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have to, like I say, as my job as a lecturer
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isn’t to give you more information but for some
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students that need a brush up on their math
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skills this might be a way to do it.
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And another extra, and again this is just
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an extra if you are struggling with your
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calculator or these kind of skills, I’ve got a
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website I will mention to you in a minute about
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an interactive calculator demonstration
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exercise.
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your calculator, be sure to check it out.
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am going to give you a specific one for the BAII
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plus, but I’ll mention that one to you and you
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can find it and if that’s not your calculator of
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course you could just Google your calculator and
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find it.
So if you are having trouble with
Or I
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Now when I am teaching a business math
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class we actually go through the simple interest
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questions one step at a time looking at each
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button that we are going to push on the
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financial calculator until every student in the
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class has it.
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it’s a great exercise.
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Sometimes it can take a while but
Actually there is a link directly from the
McGraw Hill site and the business math in Canada
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website directly to the Texas Instrument BAII
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plus calculator.
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calculator, I do like it.
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any one on the exam that you want.
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strongly recommend not a particular brand, but I
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am recommending you need a financial one.
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kind of laugh every time I see it somewhere
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saying, “Well, check your user’s manual on the
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calculator,” because the one I got, honestly it
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was about 40 pages long.
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out your calculator’s website.
And I have used that
Remember you can use
And I
I
So definitely check
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I am just going to give you an example in
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the next couple of pages of what it looks like
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for the one that I found.
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that have come to me in class, they have got
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their financial calculator and they can’t even
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change the decimal places.
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to this interactive website about your
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calculator you will actually know how to do it
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and you don’t even stop to think, it is just as
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quick.
I have known students
But once you’ve gone
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And I know I am kind of going on about this
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for a minute because many of you can just change
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anything on your phones and electronic gadgets
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in half a second so you shouldn’t have a problem
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with it, but those of you that are having a
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problem be sure to check out somewhere that you
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know how to use it well.
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subject.
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Enough of that
What else have I got for you here in this
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module for module 5?
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things.
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practice, multiple-choice in the hand out
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document, because one thing about present value,
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how you calculate it has not changed over the
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years.
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can do it, whether we’ve been using formulas or
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whether you’re using tables, but now the
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definite way to do it is from your calculator.
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So I have included lots of extra multiple-choice
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with you but they are from really old exams and
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they were calculated using tables, which means
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they only go to about 5 decimal places so they
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could be out just slightly.
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that.
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A few more introductory
One thing is I’ve got lots of extra
There has been a few different ways we
So just watch for
So again if you already know how to use
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your calculator present values is nothing, you
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won’t even need to worry about it.
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those of you that this is something new or
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you’re really rusty on, remember your best
But for
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friend is called practice, practice, practice.
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Doing the extra questions will give you the
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confidence so on exam day you’ll be just flying
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through these questions.
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ones you look forward to.
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They will be the easy
I want you to visualize the exam day, take
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ten seconds out right now and visualize the exam
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day.
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a) you’re going to feel comfortable and
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confident because you’ve practiced, or
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b) you are going to be stressed and panicking
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because you can’t remember how to make the
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calculator work for you.
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You kind of have two choices here:
As I mentioned the best way to know for
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sure you know how to make your calculator work,
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practice, practice, practice.
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Let’s look ahead.
Guess what after module
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5 you are over halfway through.
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up in the balance of the course?
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current financial assets & current financial
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liabilities.
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concepts that you are learning in module 5
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there.
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inventory valuation and cost of goods sold.
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Module 8, again we’re going to be using this
What’s coming
Module 6 is
You will have to use some of the
Module 7 is on inventory measurement,
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financial calculator, investments and financial
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instruments.
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and equipment and intangible capital assets, and
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module 10, on property, plant and equipment and
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intangibles focusing on depreciation,
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amortization and impairment.
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Module 9, is on property, plant
You’ve got this little breather in module
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5, and then just a few more concepts that
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somewhat fit together.
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Okay, we are almost finished here for the
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introduction.
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on those things since some of you will find it
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helpful and off you go to check out your
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calculator.
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I hope I didn’t nag you too much
Next. part 2 on the module summary and
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learning objectives.
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minutes almost, this is the end of FA2, Module
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5, Part 1 the introduction.
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FA2, MODULE 5, PART 2, MODULE SUMMARY & LEARNING
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And at about 12, 13
OBJECTIVES
MS. DALLAS:
FA2, Module 5 Interest Concepts, Part 2 the
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module summary and learning objective which will
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take us from slide 27 to 38.
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So the topics in module 5, an overview: the
time value of money; basic interest concepts;
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computing present and future values; the
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periodic payments required; computing the term,
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and then the computer illustration.
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huge module and they have just broken it into a
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lot of little pieces and grasping each one one
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at a time. You’re going to find this one of the
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shorter modules for you to work through.
It’s not a
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So the learning objectives, number 1, is to
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describe the concept of the time value of money;
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2, describe the concept of interest including
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simple and compound interest, and effective and
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nominal rates of interest; and 3, compute the
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present and future value of a single payment,
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and an annuity, both ordinary and annuity due;
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and 4, compute the required periodic payments
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for a given present value or future value;
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5, compute the number of periodic payments and
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the final payment required to eliminate a debt;
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and 6, design a worksheet to perform time value
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of money analysis.
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So interest concepts.
This module explains
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the fundamental concepts of interest and present
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value and future values.
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annuities due are both explained.
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techniques, including the use of a financial
Ordinary annuities and
Valuation
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calculator and functions in Excel are
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demonstrated.
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So the concept of the time value of money,
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a dollar today is worth more than a dollar
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received tomorrow because today’s dollar can be
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invested to earn interest.
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Simple and compound interest.
Interest can
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be thought of as a rent charge for the use of
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money.
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the principal amount owing only and not accrued
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interest.
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used.
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periodically and based on the principal amount
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owing plus any unpaid interest.
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compounds on itself.
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Simple interest is calculated based on
Simple interest is not very commonly
Compound interest is calculated
So the interest
A nominal rate is the stated rate of
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interest.
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that you actually pay when the effects of
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compounding are considered.
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concepts are easy to get mixed up but when we
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get to that section of the module notes I will
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make sure I clarify a bit more.
An effective rate is the annual rate
And those two
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So to determine the future and present
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values of single payments and annuities, you can
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use the calculator method or the spreadsheet
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method.
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they tell you to refer to the owner’s manual of
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your financial calculator for specific
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instructions.
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calculator method for the exam.
And of course in the module summary
And really you need to know the
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To calculate the regular payment required.
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Determining the regular payment to extinguish a
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debt by equal payments due at the end of each
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interest period and determine the regular
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payment required to accumulate a required future
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amount.
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want to retire with a million dollars how much
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do I have to save every month for the next so
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many years to do that? Great question.
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A good example here is to say, if I
And determine the regular payment required
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payable in advance, for an acquisition made on
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credit.
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regular payment meaning we want the same payment
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amounts.
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will be different.
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All of these items have, they say, a
It’s just the last payment amount that
And compute the number of periodic
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payments.
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payments plus a smaller last payment that is
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required to extinguish a debt.
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how many payments are you going to have to make
Determining the number of full
In other words
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at a certain amount before you pay off the debt?
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Well, as you can see module 5 is much
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shorter and quite a welcome relief for many of
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you.
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on for this module I believe, so you’re going to
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be busy with that.
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this as a slightly lighter module for many of
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you.
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You do have that assignment to be working
It’s kind of nice to have
At about 5 minutes slide number 38, this is
the end of FA2, module 5, part 2.
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FA2, MODULE 5, PART 3, PAST EXAM ANALYSIS
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MS. DALLAS:
FA2, module 5, interest concepts of future
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and present value, part 3, the past exam
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analysis.
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The exam blueprint indicates that 5 to 7
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percent of the exam will be from module 5.
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Usually module 5 is covered in the format of a
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few multiple-choice questions, but occasionally
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a question with journal entries has shown up on
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the exam, as you need to know the debit and
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credit portion and then from module 5 you are
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going to need to know the calculations.
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prepared for those multiple-choice questions or
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even a small question on interest and present
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values.
Be
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When I say a small question, one of the
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really old questions I saw on it was way back in
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December 2004, and I really haven’t seen one
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since then, and you won’t have access to that
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old exam so I will let you know what I mean when
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I say they’ve got a small question on it, I
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think it is worth only 7 marks.
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put it in a multiple-choice question, they laid
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it out for you.
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On January 1, a company obtained a loan of
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$250,000.
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installments including principal and compound
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interest at 8 percent.
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due at the end of the year.
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prepare an amortization schedule for the loan
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and round it to the nearest dollars, and then
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part (b) record the journal entry related to the
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But rather than
The question is pretty clear:
The loan is to be paid in three equal
And the first payment is
The required is to
st
payment made on December 31 .
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Now we haven’t seen this type of question
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for a while but it doesn’t mean something like
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that won’t come back up.
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multiple choice well I don’t think you will have
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a problem with this.
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But if you know the
The examiner felt that the overall
performance on the question was satisfactory;
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although the individual results varied
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significantly.
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that many students did well, but many students
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had no idea how to tackle the question.
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Now this leads me to believe
I have included the solution for part A,
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the little schedule for you, and there are not
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exact columns you have to do, but normally if
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you are making an amortization schedule you’d
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have the date, the amount of the payment, what’s
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the amount of the interest, so what’s the total
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payments and what’s the ending balance of the
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loan.
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that, they wouldn’t care if you had the order
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slightly out.
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it is not something that’s actually a published
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document with your financial statements that has
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to be exact.
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doing little schedules.
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And it’s not like you have to memorize
When something is just a schedule
So there is some flexibility when
And the journal entry would be a debit to
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the interest expense, a debit to the loan
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payable and a credit to the cash.
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about 4 maybe 5 marks for the schedule and 2 or
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3 marks just for the journal entry.
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So that was
Now sometimes, as I have shown from the
June 2010 question (g), sometimes the question
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will not be all just number calculating
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regarding module 5, it could be a bit theory
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based.
Such as:
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“If payments are changed from being made
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at the end of the month to the beginning
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of the month, which of the following
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would be true?
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1) The future value of a series of
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payments would decrease.
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2) The future value of a single payment
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would not change.
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3) The present value would increase; or
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4) The present value of a single payment
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would decrease.”
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Now, if I was doing this kind of question I
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would give myself a small little example.
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again if we’re making payments at the end of the
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month and we’re changing it from the end to the
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beginning, which would be true?
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answer is, three, the present value of a series
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of payments would increase.
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But
The correct
And I look at the June 2010 question (h):
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“Roman does not have any money saved for
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his retirement.
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years and he wants to have $100,000 saved
He wants to retire in 10
Copyright © The Certified General Accountants Association of British Columbia. All rights reserved.
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by that time.
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earn about 6 percent per year on his
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investments.
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at the end of each year to achieve this
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goal?”
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He thinks he is going to
How much must he contribute
So that’s a standard calculate the answer
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question.
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answer is 1) $7,587 and I will show you the
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calculation for that in just a second.
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What is the amount?
The correct
So in this module what we are trying to do
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is either calculate the present value, calculate
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the future value, calculate the amounts of the
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payments.
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So here’s another example from June 2010
question (i).
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“LIM is selling some drilling equipment
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and finally it received an offer.
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purchaser would provide a down payment of
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$50,000 and make annual payments of
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$10,000 for six years, and the first
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payment is due in one year.
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cash equivalent price of this offer,
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assuming the effective interest rate is 8
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percent?”
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The
What is the
In other words what are they really offering in
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today’s dollars?
And of course we would want that so we
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could compare it against somebody else that’s
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got a pure cash offer for us.
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and let me show you how in just a second.
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The answer is 2,
I have got those answers laid out for you
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and basically when I say payment equals $10,000,
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“N equals 6,” “I equals 8,” “present value
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equals,” you have to plug that in and calculate.
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You need to calculate the present value of all
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the amortization amount and add the $50,000 that
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they are going to pay you cash right now.
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are finding out what the stream of money that
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$10,000’s worth plus add the $50,000 they just
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gave us, that’s why the answer is $96,229 and
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not $46,229.
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So we
Notice these answers have all been rounded
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to whole dollars, if you did get some cents it
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probably means you did it correctly.
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your calculators would be preset for 6 or 9
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decimal places, which makes you have more
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accurate numbers, so good for you for that.
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Most of
So if those questions slightly challenged
24
you, good.
25
module and you’re going to spend some time
You’re going to go through the whole
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learning the material first and then you will
2
spend some time practicing.
3
feel comfortable with it and you will be ready
4
for the exam.
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And then you will
So this was just a quick little review of
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what kind of questions have been on the past
7
exams, what can you expect and what you have to
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look for as you are going through the module.
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So at about 7 minutes, this is the end of part 3
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on the past exam analysis.
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FA2, MODULE 5, PART 4, OVERVIEW AND DEFINITIONS, AND
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TOPICS 5.1 AND 5.2
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BASIC INTEREST CONCEPTS
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MS. DALLAS:
TIME VALUE OF MONEY and
FA2, Module 5, Interest concepts, Part 4.
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This section will take us from slide 50 to 74
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and covers a lot of interesting information on
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an overview of interest concepts, definitions,
18
information about the calculator and then on to
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topic 5.1, the time value of money and 5.2 on
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basic interest concepts.
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First thing I want you to make sure you
22
note is about the required reading.
23
actually not physically in the textbook and you
24
need to get to that required reading.
25
to click on the link and it is only available
It’s
You have
Copyright © The Certified General Accountants Association of British Columbia. All rights reserved.
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1
online, and that link is at the beginning of
2
topic number 1, 2 or 3.
3
chapter 8 from the textbook, but it is only
4
online.
5
It is an appendix for
And it’s actually not that long so if you
6
really wanted to print it out, you can even save
7
it to your hard drive or you can print it out or
8
whatever suits you.
9
Now on slide 52 I have the abbreviations
10
for most of the calculator terminology.
11
stands for present value; “FV" for future value;
12
“PMT” is the amount of the annuity payment; “I”
13
is the interest rate per period; “N” is the
14
number of periods.
15
of years it is the number of periods.
16
the present value, the future value, the
17
payment, the interest or N, or a “?” you should
18
be able to solve for any one of the desired
19
values.
20
“PV”
Notice it is not the number
So for
Also be aware that there is the BGN key,
21
the begin key, and you need to set your
22
calculator on that if you’re using annuity due.
23
But only if you are using an annuity due, and if
24
you are trying to use -- do a regular annuity
25
and your begin key is on, you’re in begin mode
Copyright © The Certified General Accountants Association of British Columbia. All rights reserved.
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1
2
and you’re going to get the wrong answers.
And a note of caution is you cannot just
3
clear the calculator by pressing the calculator
4
clear, you have to completely reset all of the
5
entries for the values of N, I, PV, PMT and the
6
future value.
7
clear your calculator of that and you are going
8
to have to look in the instruction manual if
9
you’re not aware of how to do it.
10
And there are certain ways to
And the good thing is that it holds
11
everything the same.
12
something, you know, with $50,000 over 5 years
13
at, let’s say the interest rate is 8 percent or
14
10 percent or 12 percent.
15
in and change “I” and press the calculate button
16
and it will do it.
17
do it.
18
So that is why the calculator doesn’t clear the
19
memory for each one of them, unless there is a
20
specific key -- I think you have press the
21
function 2 key or something like that.
22
sure you look at your calculator and know how to
23
clear all those keys.
24
25
Say we are trying to do
We can just go back
Then we change “I” again and
So it does the what if situation great.
So make
Another really important thing is called
the cash flow.
You have to enter the values
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1
into the calculator correctly.
2
as plus, and cash outflow is a minus.
3
you deposit $5,000 into the bank that’s a
4
negative, and you are thinking “What?”
5
is, it’s out of your pocket.
6
get the money back in the future it’s going to
7
be a positive.
8
the plus/minus key for this. But basically the
9
concept always is if the present value is minus
10
then the future value is positive or visa versa.
11
Because either we give the bank money and then
12
later we get the money back from the bank or the
13
bank gives us money and then we make payments
14
back to the bank.
15
always a plus and a minus.
16
Cash inflow is
So when
Well it
And then when you
So you are going to have to use
But with the cash flow it is
So again the underlying logic is that a
17
present value represents what you would pay
18
today, a cash outflow, to obtain a sum or sums
19
of money in the future, the inflows.
20
value is positive as the bank will give the
21
money back to you, so then it’s an inflow to
22
you.
23
for the bank, we’re looking at it for you.
24
outflows are negative; inflows are positive.
25
The future
We are not looking at outflows or inflows
So
So money has a different value over time
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1
because money can be put to work, and therefore
2
it earns interest.
3
Let’s look at a couple of definitions.
For
4
simple interest, it’s calculated based on the
5
original principal amount and not on any accrued
6
interest.
7
on the original amount.
8
is calculated periodically and based on the
9
original principal amount plus any unpaid
10
interest that’s been accrued since the beginning
11
of the period.
12
It just calculates the interest based
And compound interest
So it compounds.
The future value is the value that a stream
13
of money will accumulate to in the future at a
14
given compounded interest rate.
15
value is the value today of that stream of money
16
to be received sometime in the future.
17
single payment, the present value factor is
18
always less than the future value factor,
19
assuming positive interest growth rate.
20
that number there is sort of more important when
21
you are using tables and stuff, and what we’re
22
trying to say, if we’ve got a certain amount of
23
money ten years from now or five years from now,
24
any point in the future it will be worth less
25
than that now because the money is worth less
And the present
For a
And
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1
now, more in the future.
2
in the future might be $970 today, so you can
3
see that factor is less than one.
4
percent so that’s less than one.
5
to totally know that but you have to remember
6
that when you are going directions with the
7
money.
8
So a thousand dollars
It’s like 97
You don’t have
And importantly the definition of an
9
annuity.
10
of equal amounts.
11
payment is made at the beginning of the period.
12
And we will go through those details in a little
13
bit.
14
15
Annuity is a number of single payments
And annuity due is when the
FA2, MODULE 5, PART 4, TOPIC 5.1 TIME VALUE OF MONEY
So some hints I have about the time value
16
of money.
17
you’re converting everything to the present
18
value or to the future value.
19
directed, you should pretty much always be
20
calculating to the present value.
21
whether you are given the future amounts or the
22
present amount.
23
carefully in those problem style formats.
24
what they are telling you for the future or is
25
it what’s happening now?
You always have to determine whether
Unless otherwise
And determine
So you have read the question
Is
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1
2
And also determine are you given just a
single amount or an annuity?
3
And then you have to perform the
4
calculations to make the decision about the
5
problem or the case.
6
I have a few other sort of little kind of
7
rules.
8
greater the value.
9
conversely, the lesser the value of the present
10
value for a given future value.
11
longer it takes to maturity the more it is going
12
to be worth at the end.
13
The longer the time to maturity, the
And also the opposite or
Okay.
So the
And the higher the rate of interest, the
14
greater the future value will be as well.
15
the more frequent the compounding the greater
16
the future value will be as well.
17
the longer the time, the higher the rate, the
18
more frequent.
19
will be more.
And
So that means
Always the amount in the future
20
So there is sort of a relationship between
21
the present value and the future value; that is
22
the future value equals the present value times
23
one plus “I” to the “N” factor.
24
restated showing the present value.
25
It can also be
So these formulas are the basis for the
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1
above statements about the time value of money.
2
I’m really not going to go over more of the
3
formulas as I encourage you to use the
4
calculator for everything, the financial
5
calculator that is going to automatically
6
calculate everything.
7
always just use the formulas to go through it.
8
It is not recommended, and also some students
9
love to double-check their work by memorizing
10
the formulas.
11
ahead, but if not focus on your financial
12
calculator.
13
FA2, MODULE 5, PART 4, TOPIC 5.2
14
But you definitely can
If you’ve got extra time go
SIMPLE INTEREST
So topic 5.2, simple interest is rarely
15
used in business, so unless stated otherwise,
16
all interest computations are to be calculated
17
on a compound basis.
18
the compounding period is annual, unless there
19
is a specific comment to tell you otherwise.
20
And that’s general.
21
law, in Canada, we always are stating interest
22
in values that are compounded annually unless
23
they tell you otherwise that it is not annual.
24
So the method of calculating interest
25
refers to how often the interest is compounded.
And you would assume that
We almost have that rule,
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1
So it’s quite often to see lenders compounding
2
interest on a basis or daily, weekly, month,
3
semi-annually, or annually.
4
always assume it’s annual unless you are told
5
otherwise.
6
But, like I said,
And accountants are interested in the
7
number of periods, not years, that the
8
investment or loan is to be held for, and the
9
interest rate per period.
10
requires converting the nominal rate per year to
11
a more appropriate measure.
12
purposes, when we are trying to compare things,
13
it is necessary to ensure that all nominal, the
14
quoted rates of interest, are converted to the
15
effective rate, what you actually pay or receive
16
rates.
17
And this frequently
So for comparative
So be patient with yourself and almost
18
write this down, and on slide 69 it’s printed
19
out there for you.
20
quoted in the annual terms with the number of
21
compounding periods.
22
compounded quarterly.
23
as the nominal rate.
24
pay when the effects of compounding are taken
25
into rate is called the effective rate.
That the interest rates are,
For instance 10 percent
The quoted rate is known
The rate that you actually
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1
So for example, 10 percent compounded
2
quarterly is really the effective rate of 10.38
3
percent.
4
effective rate.
5
refers to the annual stated rate with
6
compounding.
7
that you actually end up receiving or paying.
8
So effectively how much?
9
important is say you have a credit card or
10
something and they tell you it’s only 2 percent
11
per month.
12
it’s really 28.8 percent per year I believe that
13
one is.
14
they are talking about on an annual basis.
15
So the nominal rate versus the
The nominal rate of interest
The effective rate is the rate
Where this is really
Well when you compound that out,
So it’s really important to know what
And if you’re trying to figure out some of
16
these things on the calculator or your
17
spreadsheet, the easier way to calculate rather
18
than using the formula every time to switch
19
between nominal to effective rates, is there are
20
some built-in functions on your calculator or
21
your spreadsheet to do it for you.
22
want to try and find those and make sure you
23
know how to use that function on your
24
calculator.
25
So you might
Like I said I almost feel kind of remiss
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1
not showing you on your calculator, but if there
2
is 10 of you out there I believe there’s at
3
least five different financial calculators.
4
we can’t really do that, but we are telling you
5
these are the important things you need to know,
6
now figure out your calculator to do that.
7
So
So on slide 73 I have kind of made a little
8
table for you.
9
$1,000 at 10 percent interest today, for 3
10
years.
11
$100 interest, so your total investment will be
12
$1,100.
13
to have a $110 interest, so you will have
14
$1,210.
15
$121 interest, so you will now have $1,331.
16
the future value of $1,000 in three years at 10
17
percent is $1,331.
18
value, the PV of $1,331 three years from now at
19
10 percent is $1,000.
20
able to go back and forth with these numbers.
21
Supposing you want to invest
So at the end of year 1, you will have a
So at the end of year 2, you’re going
So at the end of year 3, you will earn
So
Or you can say the present
So see you have to be
And we will go into a little more detail of
22
even going back and forth with the numbers, but
23
even in -- if I told you we have $1,000 today
24
and we want to have so much in the future how
25
much do we have to put in per year, or how many
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1
years are we going to have to put in for?
2
That’s what we will look at in the next part of
3
the lecture.
4
So actually at 13 minutes, this is the end
5
of FA2, Module5, Part 4, which was just the
6
overview of the definitions for topic 5.1 and
7
5.2, and quite a bit of the real details are
8
going to be in the next section coming up in
9
topics 5.3 to 5.5.
10
So again at about 13 and a half minutes
11
slide 74, this is the end of FA2, Module 5, Part
12
4.
13
FA2, MODULE 5, PART 5, TOPICS 5.3 TO 5.5, COMPUTING THE
14
PRESENT AND FUTURE VALUES, THE PERIODIC PAYMENTS
15
and CALCULATING THE TERM
16
MS. DALLAS:
FA2, Module 5, Interest Concepts, Part 5.
17
This section will take us from slide 75 to 102,
18
and Topics 5.3 to 5.5 on computing the present
19
and future values, the periodic payments, and
20
calculating the term.
21
potatoes of this module.
22
23
24
25
This is the real meat and
FA2, MODULE 5, PART 5, TOPIC 5.3 COMPUTING PRESENT AND
FUTURE VALUES
Topic 5.3.
In Topic 5.3 please note, I
have copied this directly from the module notes
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1
because I want to make sure you hear it and see
2
it, and are aware of it.
It says:
3
“While the required reading does
4
illustrate the calculation of both
5
present and future values, this topic
6
limits the balance of the discussion to
7
the calculation of present values,
8
because these are what you are most
9
likely to encounter.
10
future values also are examinable.”
11
However, note that
So you have to be able to go from present
12
values to future values or future values to
13
present, and they usually are giving you the
14
examples only calculating the present value.
15
So basically there’s like three, maybe even
16
more methods, for calculating the present value
17
and future value.
18
is the spreadsheet method; and three, is the
19
calculator method.
20
need to use the calculator method.
21
the tables were given, I am not sure for how
22
long or if they are going to be given this year,
23
actually I didn’t read up on it.
24
want to be using tables make sure you follow up
25
and call the CGA office and ask them, but I have
One is the table method; two,
And you will most likely
In the past
If you really
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1
a feeling they are not supplied anymore because
2
they are actually not part of the course
3
content.
4
administrative so I am not going to really go
5
there.
6
anymore, however it is briefly found in the
7
required reading, sort of in the other sections
8
that aren’t referred to.
9
those.
10
And like I said I am not
The module notes don’t discuss tables
So let’s not count on
The spreadsheet method, well you’re not
11
going to be taking your computer into the exam
12
so from the spreadsheet you can come up with
13
formulas and if you want to memorize those you
14
could, although I think it’s silly.
15
really want to be using your calculator.
So you
16
And as I have said, most accountants
17
nowadays rely heavily on the use of their
18
financial calculator, notice not the scientific
19
calculator, and you will be much more efficient
20
and successful in your career if you become
21
proficient with your calculator.
22
So annuity versus annuity due. It’s from
23
the required reading on page 397 where I picked
24
up these definitions for you.
25
is where the payment or receipt occurs at the
Ordinary annuity
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1
end of each interest compounding period.
2
annuity due, the payment or the receipt occurs
3
at the beginning of each compounding period.
4
call it an ordinary annuity.
5
mortgage, all of those kinds of things, loans,
6
they are all ordinary.
7
they give you the money at the beginning of the
8
month, your first payment is at the end of the
9
month.
10
And an
We
For instance a
That means your payment,
So there is a few underlying assumptions
11
that you need to be aware of for annuities.
12
amount of each payment is the same throughout
13
the entire stream of the annuity payments.
14
the payments are equally spaced.
15
monthly, quarterly or even annually.
16
interest rate is stable, that means it always
17
the same.
18
interest coincide with the payment period.
19
other words, it’s annual payment, annual
20
compounding.
21
not exist, then you have to have a more -- it’s
22
more intense, the calculation, and it all has to
23
be done manually.
24
25
The
And
It can be
The
The periods used for compounding
In
If any of these conditions does
Exhibit 5.3-1, shows the difference between
an ordinary annuity and an annuity due.
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1
Basically what the difference is is the timing
2
of the payment.
3
is at the end of the interest period, whereas
4
the annuity due, the payment is at the
5
beginning.
6
comparing the timeline with the ordinary annuity
7
and the three payments with the annuity due and
8
the three payments.
9
For the ordinary, the payment
And you can see this difference by
For some students it is a whole lot easier
10
once you visualize that picture of the time
11
chart of it.
12
there.
It makes sense of what is going on
13
And example 5.3-2 and -3 – I have reproduced
14
it on slide 82 and 83 here – but what’s basically
15
happening is for an ordinary annuity you would
16
enter in the data.
17
2500, “I” is 4, and the present value would work
18
out to be negative $23,462.68, when you’ve got
19
your calculator in your financial mode and
20
everything else has been cleared.
21
For “N” is 12, the payment is
Now if you just changed one thing, and that
22
one thing was you set your present value for an
23
annuity due, you have to set it to the BGN mode.
24
You really wouldn’t even have to change any of
25
the other numbers because they would all stay in
Copyright © The Certified General Accountants Association of British Columbia. All rights reserved.
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1
there and then you press compute for present
2
value and you’d get $24,401.
3
the beginning of the period it’s more than the
4
payments at the end of the period.
5
So if you pay at
And the reason that would make sense is if
6
you get the money at the beginning of the period
7
you’re earning interest during that period.
8
Where as if you got the money at the end of the
9
period you wouldn’t have earned interest during
10
that period.
11
So practice on your calculator.
Make sure
12
you can stick these two exact things in and come
13
up with the exact amount of monies.
14
your calculator.
15
have done the business math I literally walk
16
around and make the students all punch it in and
17
I should be able to see the exact numbers, and
18
it usually has more decimal places in it.
19
want to have it exact and make sure we walk
20
through it one step at a time, that we really do
21
get these numbers.
22
ready to move on if you can’t get these numbers.
23
Practice on
If I have a classroom, when I
And I
And honestly you are not
And quite often I find what the problem is
24
with some of the errors that are made is if
25
they, the student, does not enter the plus or
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1
the minus key correctly, or if you haven’t
2
cleared all the items to start.
3
there is this little key called the compounding
4
frequency that gets all messed up and that could
5
be a bit of the problem.
6
in the other parts, is learn your calculator.
7
Find a website for your specific calculator, try
8
and find a tutorial for it and make sure you
9
understand how your calculator works.
10
make life so much easier for you.
11
And sometimes
So as I’ve said before
It will
And for those of you who need it, I have
12
put extra practice questions with examples, how
13
to enter it in your calculator, into the
14
handouts.
15
And on slide 57 I’ve actually got it that
16
it sort of, if you look at any of these
17
textbooks that I picked up from the library on
18
business math, they show you how to exactly put
19
it in and then you use your calculator and you
20
make sure you can get the exact right answer.
21
So you might want to pause me for a second or
22
have a look at slide 57 and print those out.
23
And make sure you can get your calculator to get
24
the exact numbers.
25
So for many of you this is completely just
Copyright © The Certified General Accountants Association of British Columbia. All rights reserved.
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1
a review.
2
skimmed through the required reading, you know
3
how to use your calculators, especially those
4
people that work in banks or have taken business
5
math courses before.
6
you.
So for you folks you are lucky on this
7
one.
For other students you may have to read it
8
through two or three times.
9
words, practice.
10
11
You are going through it, you’ve
It’s just a refresher for
And as my usual
FA2, MODULE 5, PART 5, TOPIC 5.4, PERIODIC PAYMENTS REQUIRED
So topic 5.4, is for the periodic payments
12
required.
13
backwards and forth and calculate any of the
14
unknowns with the calculator.
15
Truthfully, you should be able to go
I went through the definitions earlier but
16
I’ve got it here on slide 90 again.
17
calculators come with the numbers or all of
18
these little keys all on one line, present
19
value, future value, payment, “I” or “N”.
20
I am saying to you is that it doesn’t matter
21
which of the information you’re given in the
22
problem, you should be able to calculate any of
23
the other ones.
24
should be able to calculate.
25
Now most
What
Any of those unknowns you
And truthfully, once you get a handle on it
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1
you can go back and forth and change one thing
2
and do what ifs and once you really understand
3
it and understand how it works and when you’ve
4
got to press the “enter” key and when you’ve got
5
to press the “function 2” key or the “shift
6
function key” or whatever it is on your
7
calculator, once you know the rules you will be
8
able to play the game and do a great job.
9
FA2, MODULE 5, PART 5, TOPIC 5.5, COMPUTING THE TERM
10
And again topic 5.5 is to calculate the
11
term, but once you know how to do them either
12
way you should be able to get your calculator to
13
do the exact amount and calculate the terms for
14
how long are you going to have to make these
15
payments.
16
And the tricky part is figuring out what
17
the last payment is, because the last payment is
18
very unlikely to be the same as all the other
19
payments.
20
way.
21
could find a multiple-choice question that says,
22
“How do you calculate that last payment?”
23
prepared.
24
25
It really just doesn’t work out that
So it is very likely that on the exam you
Be
Oh, I know, I remember from when I taught,
like I said business math classes, many students
Copyright © The Certified General Accountants Association of British Columbia. All rights reserved.
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1
get really frustrated, ready to throw their
2
calculator out the window, when they get
3
“error,” “error,” “error” flashing across the
4
screen, or sometimes they get little error
5
numbers.
6
and it is usually the student, it’s not the
7
calculator – is that what they do is enter the
8
present and the future values both as positive
9
numbers.
10
out now, means a bigger cash flow in later.
11
that means one of the numbers has to be negative
12
and one positive.
13
The most common error that we found –
Remember the logic again, cash flow
So
And if you are adding a payment into it
14
you’ve got to make sure the payment number
15
coincides with both of it as well otherwise you
16
get wrong numbers.
17
reason you will have an error, if you haven’t
18
got your plus/minus keys correct.
19
Okay, so the most common
And so I also want to say good luck to you,
20
for those of you who are using financial
21
calculators for the first time.
22
don’t give up, and practice until you are
23
efficient with your calculator.
24
25
Be patient,
And also I want to tell you this is value
added.
The value you are adding to yourself by
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1
knowing efficiently and correctly how to use
2
your financial calculator is huge.
3
personal life, for mortgages, for loans, in your
4
business life, knowing your financial calculator
5
is a must to be successful.
6
just seem like a minor issue, but really, the
7
confidence others will have in you because you
8
know the calculator and you understand the value
9
of money is very important.
10
In your
And it really might
One other thing I wanted to mention is the
11
past exam solutions for the multiple choice
12
answers, some of the older exams showed the
13
factors from the tables, whereas the more recent
14
exam show the calculator information.
15
answers should be the same, except if you are
16
doing an old, old exam again the factors were
17
usually only six decimal places and our
18
calculators are nine.
19
slight variation there.
20
So the
So there could be just a
And like I always say, important, don’t
21
forget to do the self-test for module 5.
22
Question 1, of course is a computer
23
question that will really help you learn some of
24
these skills that you will use in the future, I
25
am sure.
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1
FA2, MODULE 5, PART 5, TOPIC 5.6, COMPUTER ILLUSTRATION
2
Again topic 5.6 is the computer
3
illustration that will help you with that.
4
you’re not going to get a question on the exam
5
with a computer question, but you will have
6
questions like this in your life and in your
7
career, so you do want to use the computer and
8
Excel for the interest calculations.
9
And
And also, very valuable in this self-test,
10
there are about 25 multiple-choice questions.
11
And then questions 3 to 7 are also excellent
12
practice for your financial calculator, although
13
they are given to you more as little problems,
14
so you have to read and understand which is
15
which. And where the problem comes is figuring
16
out what’s the present value, which one is the
17
future value.
18
Also, I just remembered that, from the
19
textbook website, I believe, there is also some
20
multiple-choice questions there that you can use
21
to do more practice.
22
And for some of you, it is only going to
23
take you a few minutes to do each question, like
24
you should be able to do the multiple-choice
25
questions within three minutes.
So you can
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1
2
practice lots of them within an hour.
I like my quote that I have for you, and if
3
you guys are seeing the quote flashing on your
4
screen you know that that means I am almost
5
finished talking and you get to start doing your
6
practice.
7
“What we hope to do with ease, we must
8
learn first to do with diligence.”
9
Meaning that you have to very carefully do it
10
the first few times and then eventually it will
11
become easy.
12
13
And the next one I’ve got for you is Albert
Einstein:
14
“Don’t worry about your problems with
15
mathematics; I assure you mine are
16
greater.”
17
As I said, Module 5 is definitely one of the
18
shorter modules, you just have to practice doing
19
the information.
20
concepts that you have to learn, and learn your
21
calculator and then it is just up to you to do
22
some practicing.
23
There are a few shorter key
So at slide 102 and about 14 minutes, this
24
is the end of FA2, Module 5, Part 5.
25
(END OF FA2, MODULE 5, PART 5)
Copyright © The Certified General Accountants Association of British Columbia. All rights reserved.