Question

please answer all the questions

Question 2 Not yet answered Marked out of 7.00 P Flag question Sam Salvetti is planning to retire in 15 years. Money can be deposited at 10% compounded quarterly. What quarterly deposit must be made at the end of each quarter until Sam retires so that he can make a withdrawal of $4200 semiannually over the first five years of his retirement? Assume that his first withdrawal occurs at the end of six months after his retirement. Answer: Last saved at 13:57:16

Answer 1

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Term for retirement = 15 Years * 4 = 60 Quarters Interest rate = 10%*3/12 = 2.5% Per quarter Term for withdrawals = 5 Years * 2 = 10 Periods Semi annual withdrawal = $4,200 Effective annual interest rate = [1 + 1/n]n - 1 = [1 + 10% / 4] 4 - 1 = 0.1038129 = 10.38129 % Effective interest rate per semi annual period = [1 + EAR ]^(1/2) - 1 = [1 + 10.38129% ]^(1/2) - 1 = 0.050625 = 5.0625 % Per period Present value of withdrawals at retirement = Semi annual withdrawals * PVIFA(I , n) = $4,200 * PVIFA(5.0625%, 10) = $4,200 * 7.6984 = $32,333.28 Future value of quarterly deposits at retirement = Present value of withdrawals at retirement Quarterly deposits * FVIFA(I, n) = $32,333.28 Quarterly deposits * FVIFA(2.5%, 60) = $32,333.28 Quarterly deposits * 135.9916 = $32,333.28 Quarterly deposits = $32,333.28 / 135.9916 = $237.75939 = $238 Ans: $238