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Lecture Notes for Chapter 5
Chapter 5, Introduction to Valuation: The Time Value of Money.
Is possibly the mostimportant chapter in the entire course. This
chapter introduces the concepts of compoundinterest and the manners
in which to calculate every component of the compound interest
formula. This will be the basic building block for most of the
chapters we will coversubsequently.
It is extremely important that you read the entire chapter with
attention and that you understandevery single concept presented. If
you do not understand the material in this chapter, you willlikely
not understand the material in subsequent chapters. As always, if
there is anything youhave doubts on, please post a question to the
Class Questions forum under the DiscussionBoard tab of our courses
Blackboard site.
In chapter 5, you are guided through the reasoning of the basic
formula for calculating futurevalue and are given numerous examples
in which this formula or its derivations are used tocalculate a
solution.
The basic formula for future value is: FV = PV x (1+r)n
Where:PV = Present Value = the earlier amount on a time lineFV =
Future Value = the later amount on a time liner = Rate = the period
rate (usually annual) expressed as a decimaln = Number of periods
expressed in the same units as r
In the example:How much is $100 deposited at 10% annual interest
worth after 3 years?PV = $100
FV = Unknownr = 0.10n = 3Using our basic formula: FV = 100 x
(1.10)3 = $133.10
The basic FV formula is an equation with 4 terms (FV, PV, r and
n). Knowing any 3 terms, youcan solve for the remaining term.
Rearranging the basic formula:
PV = FV / ((1+r)n)r = ( FV / PV )1/n - 1n =
(ln(FV/PV))/(ln(1+r))
While these formulas are most commonly used in problems
involving money and interest, theyhave multiple applications beyond
this subject. For example, knowing that a certain botanicalplant
increases its height by one half each year, we want to know how
tall a 12 inch plant will be3 years from now. Once you recognize
this problem as a compound interest problem, you canuse our basic
formula to solve it. The height of the plant in 3 years will be 12
x (1+0.5)3 = 40.5inches. If you wanted to know how many years it
would take the plant to grow to a height of 100inches, you would
use our formula for n and solve for n=(ln(100/12)/(ln(1+0.5))
=ln(8.3333)/ln(1.5) = 2.12/0.41 = 5.23. It will take our plant 5.23
years to grow to a height of 100inches.
7/29/2019 Unit 2 Lecture Notes(1)
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There are many ways to solve compound interest formulas:
1. Algebraically: As described above
2. Using PV and FV tables: Appendix A of your textbook contains
a future value table and apresent value table. The same tables have
also been posted in a folder titled Mathematical
Tables found in the Course Documents tab of BB. You use these
tables by looking up thevalue of $1 for a certain number of periods
(leftmost column going down) and for a certain rate(topmost row
going sideways) then multiplying the value shown where your row and
columnintersect by your given PV (if finding FV) or FV (if finding
PV). To find r or n, you look in the bodyof the FV table in the
column of your given r (if finding n) or in the row of your given n
(if findingr) for the number closest to your PV/FV.
3. Using a Financial Calculator: These calculators are designed
for this purpose. While specificcalculator steps vary, all
financial calculators will let you input any 3 of the basic
formulas termsand give you a result for the fourth (see pages 124
and 125 of your textbook for an example, butkeep in mind that the
precise steps required depend on the model of the calculator you
areusing). See the resources in the Course Documents tab of BB for
one that has instructions for
several different financial calculators.
4. Spreadsheet Programs. These typically have functions that
calculate any term of the basiccompound interest equation when
given the other three. In Excel, these functions are: FV,PV, RATE
and NPER (see page 137 of your textbook and the resources in the
CourseDocuments tab of BB for some good material).
5. Online calculators: There are a number of online calculators
that will let you input any 3 of thebasic formulas terms and give
you a result for the fourth (for an example
seehttp://www.mathsisfun.com/money/compound-interest-calculator.html).
Regardless of the method you decide to use, it is extremely
important that you know how to
interpret a compound interest problem and how to calculate any
one of the basic formulasterms when you know the other three.
Common mistakes to avoid:
Know when to express the rate as a percentage and when to
express it as a decimal. Using thealgebraic method, we always
express r as a decimal (0.10 NOT 10%), however,
differentcalculators, spreadsheets and online tools may require you
to express the rate as a percentage(enter 10 if the rate is 10% NOT
0.10)
Always express both number of periods and rate in the unit of
measure equal to thecompounding period. If given a 12% rate
compounded monthly for one year, your n is 12
(months in a year) and your r is 0.01 (12% annual rate divided
by 12 months in one year). Ifgiven a 4% quarterly rate compounded
semi-annually for 3 years, your r is 8% (given rate of 4%quarterly
times 2 quarters in a semi-annual period) and your n is 6 (number
of semi-annualperiods in 3 years).
Test Your Understanding:
It is highly recommended that after thoroughly reading and
understanding chapter 5 you testyourself by attempting to solve
problems 2,6,10,14 and 18 starting on page 141 of your
http://www.mathsisfun.com/money/compound-interest-calculator.htmlhttp://www.mathsisfun.com/money/compound-interest-calculator.htmlhttp://www.mathsisfun.com/money/compound-interest-calculator.html
