Question

You want to have $2 million in real dollars in an account when you retire in 40 years. The nominal return on your investment is 9 percent and the inflation rate is 4 percent. What real amount must you deposit each year to achieve your goal?

Answer 1

Required Real Future Value = $ 2 million, Tenure of Deposits = 40 years, Nominal Rate of Return = 9 % and Inflation Rate = 4 %

Real Rate of Return = [(1+Nominal Rate of Return) / (1+Inflation Rate)] - 1 = [(1.09)/(1.04)] - 1 = 0.04808 or 4.808 %

Let the real deposits be $ P

Therefore, P x (1.04808)^(39) + P x (1.04808)^(38) + P x (1.04808)^(37) +..............+ P x (1.04808) + P = 2000000

P x [{(1.04808)^(20)-1}/{1.04808-1}] = 2000000

P x 115.287 = 2000000

P = 2000000 /115.287 = $ 17348.0097 ~ $ 17348.01