Question

A man is planning to retire in 30 years. Money Can be deposited at 12% interest compounded monthly, and it is also estimated that the future general inflation rate will be 2% per year. He wants to make annual withdrawals of $90,000 in terms of today's dollars over the 20 years of retirement. Assuming that his first withdrawal occurs at the beginning of the first year of retirement. What amount of end-of-month deposit must be made until the man retires?

Answer #1

Monthly (nominal) interest rate = 12%/12 = 1%

Number of months in 20 years = 20 x 12 = 240

Number of months in 30 years = 30 x 12 = 360

At end of year 30 (beginning of month 361), Present worth of future withdrawals ($) = 90,000 x P/A(1%, 240)

= 90,000 x 90.8194**

= 8,173,746

Required monthly deposit ($) = 8,173,746 / F/A(1%, 360) =
8,173,746 / 3494.9641** = **2,338.72**

**P/A(r%, N) = [1 - (1 + r)^{-N}] / r

P/A(1%, 240) = [1 - (1.01)^{-240}] / 0.01 = (1 - 0.0918)
/ 0.01 = 0.9082 / 0.01 = 90.8194

**F/A(r%, N) = [(1 + r)^{N} - 1] / r

F/A(1%, 360) = [(1.01)^{360} - 1] / 0.01 = (35.9496 - 1)
/ 0.01 = 34.9496 / 0.01 = 3494.9641

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