Your brother is planning for his retirement. He is currently 37 years old and pl

Question

Your brother is planning for his retirement. He is currently 37 years old and plans to retire at age 62 and live a little over age 97. He currently earns $100,000 per year and anticipates needing 80% of his income during retirement. He anticipates Social Security will provide him with $15,000 per year at age 62, leaving him with require savings to provide $65,000 annually during retirement. He believes he can earn 11 % on his investments per year. How much must your brother save at the end of each year starting at age 38, if he wants to make his last savings payment at age 62 to meet his retirement goal? Assume that he will be withdrawing his first retirement benefit at age 63 and last retirement benefit at age 97.

Explanation / Answer

Answer:

Total number of years for saving = 25 years (62 years - 37 years)

Total number of years of retirement = 35 years (97 - 62)

To calculate the amount to be invested every year during workinh life to earn $ 65,000 every year during retirement we shall equate present value of annuity of $ 65,000 for 35 years of retirement with the Future value of annuity of annual savings, that is;

P1 x [(1+r)n1 - 1] / r = P2 x [1 - (1+r)-n2 ] / r

here, r = 0.11; n1 = 25; n2 = 35; P1 = ? and P2 = $ 65,000

P1 x [(1+0.11)25 - 1] = $ 65,000 x [1 - (1+0.11)-35] or P1 = $ 65,000 (1-0.025924) / (13.58546 - 1) or P1 = $ 63,315 / 12.58546 or P1 = $ 5031

Therefore, one shall invest $ 5031 per year.

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