1. Present value of an annuity Consider the following cases. Calculate the present value of the
annuity, assuming that it is An ordinary annuity. An annuity due. Compare your findings in parts
a(1) and a(2). All else being identical, which type of annuity-ordinary or annuity due-is
preferable? Explain why.
Solution
Case Amount of annuity Interest rate Period PV at ordinary annuity PV at annuity due
Difference A 12000 7% 3 $31,491.79 $33,696.22 $2,204.43 B 55000 12% 15 $374,597.55
$419,549.25 $44,951.71 C 700 20% 9 $2,821.68 $3,386.01 $564.34 D 140000 5% 7
$810,092.28 $850,596.89 $40,504.61 E 22500 10% 5 $85,292.70 $93,821.97 $8,529.27 in
general, if you're the one making the payments, you're better off with an ordinary annuity. If
you're the one receiving the payments, you're better off with an annuity due. The reason lies in
a basic principle of finance known as the "time value of money": Because of inflation and the
ability to earn interest on invested or banked money, a sum of money today is worth more than
the same sum in the future. The longer you can delay making your first fixed payment, the less
that payment costs you. On the flip side, the earlier you can receive the first payment of an
annuity, the more it's worth. Practically speaking, though, once an annuity begins, the cash
flows occur on the same schedule, and there's little noticeable difference between an ordinary
annuity and an annuity due.