Principles of Managerial Finance

164 PART 2 Important Financial Concepts

$1,000 $1,000 $1,000 $1,000 $1,000

012345

$1,311

1,225

1,145

1,070

1,000

$5,751 Future Value

End of Year

8. A mathematical expression that can be applied to calculate the future value interest factor for an ordinary annuity
   more efficiently is
   FVIFAi,n[(1i)n1] (4.13a)
   The use of this expression is especially attractive in the absence of the appropriate financial tables and of any finan-
   cial calculator or personal computer and spreadsheet.

^1

i

future value interest factor
for an ordinary annuity
The multiplier used to calculate
the future value of an ordinary
annuityat a specified interest
rate over a given period of time.

Time line for future
value of an ordinary
annuity ($1,000 end-of-
year deposit, earning
7%, at the end of 5
years)

EXAMPLE Fran Abrams wishes to determine how much money she will have at the end of 5

years if he chooses annuity A, the ordinary annuity. It represents deposits of

$1,000 annually, at the end of eachof the next 5 years, into a savings account

paying 7% annual interest. This situation is depicted on the following time line:

As the figure shows, at the end of year 5, Fran will have $5,751 in her account.

Note that because the deposits are made at the end of the year, the first deposit

will earn interest for 4 years, the second for 3 years, and so on.

Using Computational Tools to Find

the Future Value of an Ordinary Annuity

Annuity calculations can be simplified by using an interest table or a financial cal-

culator or a computer and spreadsheet. A table for the future value of a $1 ordi-

nary annuityis given in Appendix Table A–3. The factors in the table are derived

by summing the future value interest factors for the appropriate number of years.

For example, the factor for the annuity in the preceding example is the sum of the

factors for the five years (years 4 through 0): 1.3111.2251.1451.070

1.0005.751. Because the deposits occur at the end of each year, they will earn

interest from the end of the year in which each occurs to the end of year 5. There-

fore, the first deposit earns interest for 4 years (end of year 1 through end of year

5), and the last deposit earns interest for zero years. The future value interest fac-

tor for zero years at any interest rate, FVIFi, 0 , is 1.000, as we have noted. The for-

mula for the future value interest factor for an ordinary annuitywhen interest is

compounded annually at ipercent for nperiods, FVIFAi,n, is^8

FVIFAi,n

n

t 1

(1i)t^1 (4.13)