Annuity A has 15 payments Annuity B has 10 payments All else

Annuity A has 15 payments, Annuity B has 10 payments. All else equal, which of the following is true? a. Annuity A must have the lower present value because \"t\" is higher. b. Annuity A must have the higher present value because \"t\" is higher. c. Annuity B must have the lower present value becuase \"t\" is lower. d. Annuity B must have the higher present value because \"t\" is lower.

Solution

Suppose the payment amount is $1,000 @ 10%

Annuity A,

Present Value = $1,000 * PVAF(10%,15y)

= $1,000 * 7.606 = $7,606

Annuity B,

Present Value = $1,000 * PVAF(10%,10y)

= $1,000 * 6.145 = $6,145

Answer :

b. Annuity A must have the higher present value because \"t\" is higher.

c. Annuity B must have the lower present value becuase \"t\" is lower.