Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 74.00. 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 74.0 when he fully retires, he will begin to make annual withdrawals of $105,528.00 from his retirement account until he turns 85.00. After this final withdrawal, he wants $1.36 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 10.00% interest rate.
Answer format: Currency: Round to: 2 decimal places
Given that,
Derek need FV = $1360000 in his account on his 85nd birthday and yearly withdrawal before that are PMT = $105528
interest rate r = 10%
So, amount he needed in account in his 74th birthday is calculated using PV formula of annuity
V75 = PMT*(1 - (1+r)^-t)/r + FV/(1+r)^t = 105528*(1 - 1.1^-11)/0.1 + 1360000/1.1^11 = $1162082.50
So, Value of this amount on his 65th birthday is
V65 = V74/(1+r)^(74-65) = 1162082.5/1.1^9 = $492836.42
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) = 492836.42*0.1/(1.1^40 - 1) = $1113.52
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