Question

A 9-year annuity of 18 $8,800 semiannual payments will begin 10.5 years from now, with the first payment coming 11 years from now. If the discount rate is 12 percent compounded semiannually, what is the value of this annuity nine years and seven years from now? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) Value of the annuity Nine years $ Seven years $ What is the value of the annuity today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Value today $

Answer 1

Semiannual payment = $8,800
Number of payments = 18
Annual interest rate = 12%
Semiannual interest rate = 6%

First payment is made after 11 years

Value of annuity 9 years from now = $8,800/1.06^4 + $8,800/1.06^5 + .... + $8,800/1.06^21
Value of annuity 9 years from now = $8,800 * (1/1.06)^3 * (1 - (1/1.06)^18) / 0.06
Value of annuity 9 years from now = $8,800 * 9.091065
Value of annuity 9 years from now = $80,001.37

Value of annuity 7 years from now = $8,800/1.06^8 + $8,800/1.06^9 + .... + $8,800/1.06^25
Value of annuity 7 years from now = $8,800 * (1/1.06)^7 * (1 - (1/1.06)^18) / 0.06
Value of annuity 7 years from now = $8,800 * 7.200975
Value of annuity 7 years from now = $63,368.58

Value of annuity today = $8,800/1.06^22 + $8,800/1.06^23 + .... + $8,800/1.06^39
Value of annuity today = $8,800 * (1/1.06)^21 * (1 - (1/1.06)^18) / 0.06
Value of annuity today = $8,800 * 3.184998
Value of annuity today = $28,027.98