Question

Please answer all 3 parts so I can get full credit for this 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?

b. What is the value three years from now?

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

Annual interest rate = 8.00%
Monthly interest rate = 8.00% / 12
Monthly interest rate = 0.6667%

Effective annual rate = (1 + Monthly interest rate)^12 - 1
Effective annual rate = (1 + 0.006667)^12 - 1
Effective annual rate = 1.0830 - 1
Effective annual rate = 0.0830 or 8.30%

Semiannual interest rate = (1 + Effective annual rate)^(1/2) - 1
Semiannual interest rate = (1 + 0.0830)^(1/2) - 1
Semiannual interest rate = 1.04067 - 1
Semiannual interest rate = 0.04067 or 4.067%

Answer a.

Semiannual payment = $5,900
Number of payments = 10

Value of annuity 5 years from now = $5,900/1.04067^9 + $5,900/1.04067^10 + … + $5,900/1.04067^17 + $5,900/1.04067^18
Value of annuity 5 years from now = $5,900 * (1/1.04067)^8 * (1 - (1/1.04067)^10) / 0.04067
Value of annuity 5 years from now = $5,900 * 5.876479
Value of annuity 5 years from now = $34,671.23

Answer b.

Value of annuity 3 years from now = $34,671.23/1.04067^4
Value of annuity 3 years from now = $29,560.86

Answer c.

Value of annuity today = $29,560.86/1.04067^6
Value of annuity today = $23,272.28