Question

A 5-year annuity of ten $9,000 semiannual payments will begin 8 years from now, with the first payment coming 8.5 years from now. a. If the discount rate is 6 percent compounded monthly, what is the value of this annuity 2 years from now? b. What is the current value of the annuity? as went is recurent value

Answer 1

Annual interest rate = 6.00%
Monthly interest rate = 6.00% / 12
Monthly interest rate = 0.50%

Effective annual rate = (1 + Monthly interest rate)^12 - 1
Effective annual rate = (1 + 0.005)^12 - 1
Effective annual rate = 1.06168 - 1
Effective annual rate = 0.06168 or 6.168%

Semiannual interest rate = (1 + Effective annual rate)^(1/2) - 1
Semiannual interest rate = (1 + 0.06168)^(1/2) - 1
Semiannual interest rate = 1.03038 - 1
Semiannual interest rate = 0.03038 or 3.038%

Answer a.

Semiannual payment = $9,000
Number of payments = 10

Value of annuity 2 years from now = $9,000/1.03038^13 + $9,000/1.03038^14 + … + $9,000/1.03038^21 + $9,000/1.03038^22
Value of annuity 2 years from now = $9,000 * (1/1.03038)^12 * (1 - (1/1.03038)^10) / 0.03038
Value of annuity 2 years from now = $9,000 * 5.944954
Value of annuity 2 years from now = $53,504.59

Answer b.

Value of annuity today = $53,504.59/1.03038^4
Value of annuity today = $47,468.05