Question

Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 72.00. During these years of part-time work, he will neither make deposits to nor take withdrawals from his retirement account. Exactly one year after the day he turns 72.0 when he fully retires, he will begin to make annual withdrawals of $122,438.00 from his retirement account until he turns 87.00. He will make contributions to his retirement account from his 26th birthday to his 65th birthday. To reach his goal, what must the contributions be? Assume a 7.00% interest rate.

Answer 1

First, we find the present value for the withdrawals at the start of year 72

Using a financial calculator

FV = 0

PMT = 122438

N = 15 (87years-72years = 15 years)

I/Y = 7

cpt PV, we get PV = 1115154.77

Equivalent present value of this amount at the 65th birthday = 1115154.77/(1.07^7) = $694462.35

This amount should be equal to the future value of savings

Using a financial calculator

PV = 0

FV = 694462.35

N = 40(65years-25years = 40 years)

I/Y = 7

cpt PMT, we get PMT = 6333.20

Hence, his contributions should be equal to $6333.20