Question

A racehorse breeder wants to set up a perpetual prize for a racing event in his name. The first race will be run and the first prize will be paid two years from now when he retires. The fund is established immediately and will earn an effective rate of 4.0% per annum. The annual prize will be $262183. How much should he deposit into the fund? Give you answer correct to the nearest cent.

Answer 1

Perpetual Annual Prize (beginning at t=2) = $ 262183 and Effective Interest Rate = 4 %

Present Value (PV) at the end of Year 1 = 262183 / 0.04 = $ 6554575

In order for the current deposit to be enough for the perpetual racehorse price, the future value of the current deposit a year from now should equal the present value of the perpetual race prize at t=1, compounded at the effective interest rate of 4%.

Therefore, Current Deposit X (1.04) = 6554575

Current Deposit = 6554575 / 1.04 = $ 6302475.962 ~ $ 6302475.96