A couple will retire in 50 years; they plan to spend about $22,000 a year in ret

Question

A couple will retire in 50 years; they plan to spend about $22,000 a year in retirement, which should last about 25 years. They believe that they can earn 8% interest on retirement savings. But now assume that the inflation rate over the next 50 years will average 4.2%.

a. What is the real annual savings the couple must set aside?

b. How much do they need to save in nominal terms in the first year?

c. How much do they need to save in nominal terms in the last year?

d. What will be their nominal expenditures in the first year of retirement? AND The last year of retirement?

Explanation / Answer

Retirement            50.00 years Interest rate 8.00% Yearly spending $ 22,000.00 Time            25.00 years Inflation rate 4.20% Solution: a. Real interest rate = 3.65% PV of the required real savings = $356,761.22 Real annual savings = $    2,602.10 b. Real annual savings $    2,602.10 Nominal savings in year 1 = $    2,711.39 c. Real annual savings $    2,602.10 Nominal savings in the last year = $ 20,356.80 d. Nominal expenditures in the first year of retirement = $179,339.66 Nominal expenditures in the last year of retirement = $481,395.03

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