Question

Suppose you are going to receive $13,500 per year for five years. The appropriate interest rate is 8 percent.

a-1. What is the present value of the payments if they are in the form of an ordinary annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

a-2. What is the present value of the payments if the payments are an annuity due? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

b-1. Suppose you plan to invest the payments for five years. What is the future value if the payments are an ordinary annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

b-2. What is the future value if the payments are an annuity due? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

c-1. Which has the higher present value, the ordinary annuity or annuity due?

c-2. Which has the higher future value?

Answer 1

Answer a.

Annual payment = $13,500
Time period = 5 years
Interest rate = 8%

Present value of ordinary annuity = $13,500/1.08 + $13,500/1.08^2 + $13,500/1.08^3 + $13,500/1.08^4 + $13,500/1.08^5
Present value of ordinary annuity = $13,500 * (1 - (1/1.08)^5) / 0.08
Present value of ordinary annuity = $13,500 * 3.99271
Present value of ordinary annuity = $53,901.59

Present value of annuity due = $13,500 + $13,500/1.08 + $13,500/1.08^2 + $13,500/1.08^3 + $13,500/1.08^4
Present value of annuity due = $13,500 * 1.08 * (1 - (1/1.08)^5) / 0.08
Present value of annuity due = $13,500 * 4.31213
Present value of annuity due = $58,213.76

Answer b.

Annual payment = $13,500
Time period = 5 years
Interest rate = 8%

Future value of ordinary annuity = $13,500*1.08^4 + $13,500*1.08^3 + $13,500*1.08^2 + $13,500*1.08 + $13,500
Future value of ordinary annuity = $13,500 * (1.08^5 - 1) / 0.08
Future value of ordinary annuity = $13,500 * 5.86660
Future value of ordinary annuity = $79,199.10

Future value of annuity due = $13,500*1.08^5 + $13,500*1.08^4 + $13,500*1.08^3 + $13,500*1.08^2 + $13,500*1.08
Future value of annuity due = $13,500 * 1.08 * (1.08^5 - 1) / 0.08
Future value of annuity due = $13,500 * 6.33593
Future value of annuity due = $85,535.06

Answer c.

Annuity due has the higher present value.
Annuity due has the higher future value.