Fundamentals of Financial Management (Concise 6th Edition)

136 Part 2 Fundamental Concepts in Financial Management

A B C D E F G

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Payment amount

Interest rate

No. of periods

=

=

=

=

=

=

$100.00

5.00%

3

PMT

I

N

Periods:

Cash Flow Time Line:

0

!$100 !$100 !$100

!$100.00

!$105.00

!$110.25

!$315.25

Step-by-Step Approach.

Multiply each payment by

(1"I)N!t and sum these FVs to

!nd FVAN:

1 2 3

$315.25

Formula Approach:

FVAN = PMT #! "

Calculator Approach:

Excel entries correspond with these calculator keys:

Excel Function Approach: Fixed inputs:

Cell references:

N I/YR PV PMT

3 5 $0 !$100.00

FV

$315.25

=FV(0.05,3,! 100 , 0 ) = $315.25

=FV(C132,C133,!C131, 0 ) = $315.25

I/YR N PMT PV FV

FVAN =

FVAN =

! 1 " I" =

N! 1

I

Tabl e 5 - 3 Summary: Future Value of an Ordinary Annuity

We can generalize and streamline the equation as follows:

FVAN! PMT(1 " I)N#^1 " PMT(1 " I)N#^2

" PMT(1 " I)N#^3 "... " PMT(1 " I)^0

5-3! PMT # (1 " I)

N # 1

__I (^) $
The! rst line shows the equation in its long form. It can be transformed to the sec-
ond form, which can be used to solve annuity problems with a non! nancial calcu-
lator.^5 This equation is also built into! nancial calculators and spreadsheets. With
an annuity, we have recurring payments; hence, the PMT key is used. Here’s the
calculator setup for our illustrative annuity:
N I/YR PV PMT FV
3 5 0 –100 End Mode
315.25
We enter PV! 0 because we start off with nothing, and we enter PMT! $ 100
because we plan to deposit this amount in the account at the end of each year.
When we press the FV key, we get the answer, FVA 3! 315.25.
Because this is an ordinary annuity, with payments coming at the end of each
year, we must set the calculator appropriately. As noted earlier, calculators “come
out of the box” set to assume that payments occur at the end of each period, that
is, to deal with ordinary annuities. However, there is a key that enables us to switch
between ordinary annuities and annuities due. For ordinary annuities, the desig-
nation is “End Mode” or something similar, while for annuities due, the designator
(^5) The long form of the equation is a geometric progression that can be reduced to the second form.