Question

What amount of money should be set aside today to provide 40 payments of $10,000 every six months if the first payment is to be made in 20 years from now and money is invested at 9% compounded semiannually? Cannot use Excel

Answer 1

No. of payments	40
payment frequency	semi annual
Payment starting from (in half years)	40
Payment period (in half years)	40 - 80
Interest rate	9%
Semi annual rate	4.50%
Cashflows	10000

PV factor computation for payments starting 40th half year upto 80th half year

PV factor = PV annuity factor for 80 half year payments - PV annuity factor for 39th half year payments

PV factor = ((1-(1+semi annual rate)^-80)/semi annual rate - ((1-(1+semi annual rate)^-39)/semi annual rate

PV factor = ((1-(1+4.5%)^-80)/4.5% - ((1-(1+4.5%)^-39)/4.5%

PV factor = 21.5653 - 18.2297

PV factor = 3.3356

Present value of half year payments = Half year payments x PV factor

Present value of half year payments = Half year payments x 3.3356

Present value of half year payments = 10000 x 3.3356

Present value of half year payments = $33,356 ---> Amount to be set aside today

Hope this helps you answer the question. Please provide your feedback or rating on the answer.

Thanks