Principles of Managerial Finance

CHAPTER 4 Time Value of Money 165

5750.74

1000 PMT
N

CPT

FV

I

5

7

Solution

Input Function

This factor is the multiplier used to calculate the future value of an ordinary

annuityat a specified interest rate over a given period of time.

Using FVAnfor the future value of an n-year annuity, PMTfor the amount to

be deposited annually at the endof each year, and FVIFAi,nfor the appropriate

future value interest factor for a one-dollar ordinary annuity compounded ati

percent fornyears,we can express the relationship among these variables alterna-

tively as

FVAnPMT(FVIFAi,n) (4.14)

The following example illustrates this calculation using a table, a calculator, and

a spreadsheet.

EXAMPLE As noted earlier, Fran Abrams wishes to find the future value (FVAn) at the end

of 5 years (n) of an annual end-of-year depositof $1,000 (PMT) into an account

paying 7% annual interest (i) during the next 5 years.

Table Use The future value interest factor for an ordinary 5-year annuity at 7%

(FVIFA7%,5yrs), found in Table A–3, is 5.751. Using Equation 4.14, the $1,000

deposit5.751 results in a future value for the annuity of $5,751.

Calculator Use Using the calculator inputs shown at the left, you will find the

future value of the ordinary annuity to be $5,750.74, a slightly more precise

answer than that found using the table.

Spreadsheet Use The future value of the ordinary annuity also can be calculated

as shown on the following Excel spreadsheet.

Finding the Present Value of an Ordinary Annuity

Quite often in finance, there is a need to find the present value of a streamof cash

flows to be received in future periods. An annuity is, of course, a stream of equal

periodic cash flows. (We’ll explore the case of mixed streams of cash flows in a

later section.) The method for finding the present value of an ordinary annuity is

similar to the method just discussed. There are long and short methods for mak-

ing this calculation.