Question

Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 71.00. 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 71.0 when he fully retires, he will begin to make annual withdrawals of $161,481.00 from his retirement account until he turns 87.00. He 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 9.00% interest rate.

Answer 1

Derek will start making annual withdrawal 1 year after he turns 71 for 16 years until age 87.

Firstly we will calculate the Present Value of withdrawal at age 71 and then discounting it for 6 years to arrive at the Present value at age 65.

Calculating the Present Value at age 65:-

Where, C= Periodic withdrawal = $161,481

r = Periodic Interest rate = 9%

n= no of periods = 16

m = no of periods of discounting = 6

Present Value at age 65 = $800,381.68

Now, from age 26 to age 65 Derek will deposit annually to accumuale the above amount at age 65.

Calculating the Annual Deposits:-

Where, C= Periodic Annual Deposits

r = Periodic Interest rate = 9%

n= no of periods = 40 payments (From 26th to 65th)

C = $2,368.82

So, Derek's annual contribution must be $2368.82

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