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144 PART 2 Important Financial Concepts
Time line for future
value of an ordinary
annuity ($1,000 end-ofyear
deposit, earning
7%, at the end of 5
years)
TABLE 4.1 Comparison of Ordinary Annuity
and Annuity Due Cash Flows
($1,000, 5 Years)
Annual cash flows
End of year a Annuity A (ordinary) Annuity B (annuity due)
0 $ 0 $1,000
1 1,000 1,000
2 1,000 1,000
3 1,000 1,000
4 1,000 1,000
5
1 , 0 0 0 0
Totals $
5 , 0 0 0 $
5 , 0 0 0 aThe ends of years 0, 1, 2, 3, 4, and 5 are equivalent to the beginnings of years
1, 2, 3, 4, 5, and 6, respectively.
Finding the Future Value of an Ordinary Annuity
The calculations required to find the future value of an ordinary annuity are illustrated
in the following example.
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 each of the next 5 years, into a savings account
paying 7% annual interest. This situation is depicted on the following time line:
$1,000 $1,000 $1,000 $1,000 $1,000
0 1 2 3 4 5
End of Year
$1,311
1,225
1,145
1,070
1,000
$5,751 Future Value
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.