Introduction to Finance

248
Annuity Due Applications
LO 9.10
Understand and calculate annuity due problems involving future and present values. 
9.10
Annuity Due Problems
Future Value of an Annuity Due
In contrast with an ordinary annuity, an 
annuity due
exists when the equal periodic payments 
occur at the beginning of each period. Let’s return to the example used in the Future Value 
of an Annuity section in this chapter. Recall that the problem involved a three-year annuity, 
$1,000 annual payments, and an 8 percent interest rate. However, let’s assume that the fi rst 
payment now is made at the beginning of the fi rst year, namely at time zero. This will allow 
the fi rst $1,000 payment to earn interest for three years, the second payment to earn interest 
for two years, and the third payment to earn interest for one year.
The calculation process to fi nd the future value of this annuity due problem can be demon-
strated as follows:
FV annuity due = $1,000(1.08)
3
+ $1,000(1.08)
2
+ $1,000(1.08)
1
= $1,000(1.260) + $1,000(1.166) + $1,000(1.080)
= $1,000(1.260 + 1.166 + 1.080)
= 
$1,000(3.506)
= 
$3,506
Notice that by making the fi rst payment now, the future value of this annuity at the end of 
three years will be $3,506. This contrasts with a future value of $3,246 if payments are delayed 
by one year, as would be the case with an ordinary annuity.
Table-based Solution:
Equation 9.6 can be easily modifi ed to handle annuity due problems as follows:
FVAD
n
= PMT(FVIFA
r
,
n
)(1 + 
r
) (LE9.1)
where FVAD is the future value of an annuity due and the (1 + 
r
) factor eff ectively compounds 
each payment by one more year to refl ect the fact that payments start at the beginning of each 
period. In this problem, the annual payment is $1,000, the time period is three years, and the 
interest rate is 8 percent. Using equation LE9.1, the future value of this annuity due would be,
FVAD
3
= $1,000(FVIFA
8%,3
)(1 + 0.08)
= 
$1,000(3.246)(1.08)
= 
$1,000(3.506)
= 
$3,506
The FVIFA of 3.246 comes from Table 9.3 at the intersection of the 8 percent interest rate 
column and the year-three row.
Annuity due problems also can be solved with fi nancial calculators. In fact, most fi nancial 
calculators have a DUE key (or a switch) for shifting payments from the end of time periods 
to the beginning of time periods. If you have a fi nancial calculator, you can verify the future 
value of an annuity due result for the three-year annuity problem. First, clear the calculator. 
Next, enter –1000 (for both TI and HP calculators) and press the PMT key. Then enter 8 
and press the %i key, and enter 3 and press the N key. Finally, instead of pressing the CPT 
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