Question

Assuming a 12% annual interest rate, determine the present value of a five-period annual annuity of $3,500 under each of the following situations:

a. The first payment is received at the end of the first year, and interest is compounded annually.
b. The first payment is received at the beginning of the first year, and interest is compounded annually.
c. The first payment is received at the end of the first year, and interest is compounded quarterly.

Answer 1

a. The first payment is received at the end of the first year, and interest is compounded annually.

present value = annual payment x PVIFA

annual payment = $3,500

PVIFA, 12%, 5 periods = 3.6048

present value = $12,616.80

b. The first payment is received at the beginning of the first year, and interest is compounded annually.

annual payment = $3,500

PVIF annuity due, 12%, 5 periods = 4.0373

present value = $14,130.55

c. The first payment is received at the end of the first year, and interest is compounded quarterly.

present value = annual payment x PVIFA

annual payment = $3,500

effective interest rate = 1.03⁴ - 1 = 12.55%

PVIFA, 12.55%, 5 periods = 3.5562

present value = $12,446.70