Question

A five-year annuity of ten $5,900 semiannual payments will begin 9 years from now, with the first payment coming 9.5 years from now. The discount rate is 8 percent compunded monthly.

a.	What is the value of this annuity five years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b.	What is the value three years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
c.	What is the current value of the annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Semiannual payments = $5,900
Number of payments = 10
Annual interest rate = 8.00%
Monthly interest rate = 0.6667%

First payment is made 9.50 years from now

Value of annuity 5 years from now = $5,900/1.006667^9 + $5,900/1.006667^10 + … + $5,900/1.006667^17 + $5,900/1.006667^18
Value of annuity 5 years from now = ($5,900/1.006667^8) * (1 - (1/1.006667)^10) / 0.006667
Value of annuity 5 years from now = $5,900 * 9.143666
Value of annuity 5 years from now = $53,947.63

Value of annuity 3 years from now = $53,947.63/1.006667^4
Value of annuity 3 years from now = $52,532.62

Value of annuity today = $52,532.62/1.006667^6
Value of annuity today = $50,479.39