Question

A 7-year annuity of fourteen $10,600 semiannual payments will begin 9 years from now, with the first payment coming 9.5 years from now. The discount rate is 9 percent compounded 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 annuity?

Answer 1

Semi-annual payment of Annuity = $10,600

Time Period = 7 years

Discount rate = 9% monthly

Calculating Semi-annual interest rate,

EAR = (1 + 0.09/12)¹² - 1 = 9.38%

APR(semi-annual) = 2[(1.0938)^1/2 - 1] = 9.17%

Value of Annuity(end of 9 years) = P[1 - (1 + r)^-n]/r

Value of Annuity(end of 9 years) = 10,600[(1 - (1 + 0.0917/2)^-14)]/(0.0917/2)

Value of Annuity(end of 9 years) = $107,766

Value of Annuity(end of 5 years) = 107,766/(1.0938)⁴ = $75,288.75

Value of Annuity(end of 3 years) = 107,766/(1.0938)⁶ =$62,929.50

Value of Annuity(today) = 107,766/(1.0938)⁹ =$48,088.42