Question

1. Mr. Hall wants to receive $45,000 at the end of each year in today’s dollars for the next 15 years. He is concerned about inflation and wants you to determine the lump sum he would need if the annual rate of inflation averages four percent and he could earn nine percent on his investment.

   	A.	$407,085
   	B.	$495,967
   	C.	$473,216
   	D.	$462,689
   	E.	None of the above

Answer 1

Answer is $473,216

Nominal Return = 9.00%
Inflation Rate = 4.00%

Real Return = (Nominal Return - Inflation Rate) / (1 + Inflation Rate)
Real Return = (0.09 - 0.04) / (1 + 0.04)
Real Return = 0.048077 or 4.8077%

Annual Payment = $45,000
Number of Payments = 15

Present Value = $45,000/1.048077 + $45,000/1.048077^2 + ... + $45,000/1.048077^14 + $45,000/1.048077^15
Present Value = $45,000 * (1 - (1/1.048077)^15) / 0.048077
Present Value = $45,000 * 10.5159024
Present Value = $473,216

So, he needs a lump sum amount of $473,216