Question

Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 75.00. 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 75.0 when he fully retires, he will begin to make annual withdrawals of $196,714.00 from his retirement account until he turns 85.00. After this final withdrawal, he wants $1.64 million remaining in his account. 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 8.00% interest rate.

Please round answer to 2 decimal places. :)

Answer 1

Given that,

Derek need FV = $1640000 in his account on his 85nd birthday and yearly withdrawal before that are PMT = $196714

interest rate r = 8%

So, amount he needed in account in his 75th birthday is calculated using PV formula of annuity

V75 = PMT*(1 - (1+r)^-t)/r + FV/(1+r)^t = 196714*(1 - 1.05^-10)/0.08 + 1640000/1.08^10 = $2079604.27

So, Value of this amount on his 65th birthday is

V65 = V75/(1+r)^(75-65) = 2079604.27/1.08^10 = $963259.16

He will make contribution in the account from 26th birthday to 65th birthday

So, total number of investment made N = 65-25 = 40

annual contribution = V65*r/((1+r)^N - 1) = 963259.16*0.08/(1.08^40 - 1) = $3718.34