Question

Your father is 50 years old and will retire in 10 years. He expects to live for 25 years after he retires, until he is 85. He wants a fixed retirement income that has the same purchasing power at the time he retires as $40,000 has today. (The real value of his retirement income will decline annually after he retires.) His retirement income will begin the day he retires, 10 years from today, at which time he will receive 24 additional annual payments. Annual inflation is expected to be 3%. He currently has $180,000 saved, and he expects to earn 7% annually on his savings. The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the question below.

How much must he save during each of the next 10 years (end-of-year deposits) to meet his retirement goal? Do not round your intermediate calculations. Round your answer to the nearest cent.

Answer 1

Nominal value of the annual income required on retirement = 40,000 x (1 + i)ⁿ = 40,000 x (1 + 3%)¹⁰ = 53,756.66

Hence, the retirement kitty size = PV (Rate, Nper, PMT, FV, Type) = PV (7%, 25, -53756.66, 0, 1) =  670,309.69

Of which contribution from the current saving = 180,000 x (1 + r)ⁿ = 180,000 x (1 + 7%)¹⁰ = 354,087.24

Hence, the remaining kitty size = 670,309.69 - 354,087.24 =  316,222.44

Let's say he saves an amount A during each of the next 10 years (end-of-year deposits) to meet his retirement goal.

hence, A x FV (Rate, Nper, PMT, PV) = 316,222.44

Or, A x FV (7%, 10, 1, 0) = 316,222.44

Or, 13.82A = 316,222.44

Hence, A = 316,222.44 / 13.82 = 22,887.39 = the amount he needs to save during each of the next 10 years (end-of-year deposits) to meet his retirement goal.