You plan to retire at age 40 after a highly successful but short career. You wou

Question

You plan to retire at age 40 after a highly successful but short career. You would like to accumulate enough money by age 40 to withdraw $229,000 per year for 40 years. You plan to pay into your account 15 equal installments beginning when you are 25 and ending when you are 39. Your account bears interest of 14 percent per year Use Table for your reference. (Use appropriate factor(s) from the tables provided.) Required 1. How much do you need to accumulate in your account by the time you retire? (Round your final answer to the nearest dollar amount.) nt to be accumulated in your account 2. How much do you need to pay into your account in each of the 15 equal installments? (Round your final answer to 2 decimal places.) ann1 ????? ual installment

Explanation / Answer

1) Amount to be accumulated in account $ 16,27,054 Working: Amount to be accumulated in account = Present Value of withdrawls = Annual withdrawl*Present valu of annuity of 1 = $          2,29,000 *    7.10504 = $       16,27,054 Present value of annuity of 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.14)^-40)/0.14 i 14% =               7.10504 n 40 2) Annual installment = Accumulated amount/Future value of annuity of 1 = $ 16,27,054 /             49.98035 = $ 32,553.88 Working: Annual installment = Accumulated amount at the age of year 40/Future Value of annuity due of 1 = = Future Value of annuity due of 1 = ((((1+i)^n)-1)/i)*(1+i) Where, = ((((1+0.14)^15)-1)/0.14)*(1+0.14) i 14% =             49.98035 n 15

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