Question

You plan to retire at age 65. After learning the concept of time value of money, you decide to start saving for retirement. Today, you are 20 years old and will put $20,000 in your retirement savings account. You are also planning on making an annual deposit at 6% of your salary. However, you realize that you just got your job and can’t start making the first deposit until exactly four years from today. You are making a salary of $60,000 per year and will remain at such for as long as you work. You want to start making withdraws starting one year from retirement and hope for an equal amount every year to cover your living expenses until age 99. Assume the annual rate of return has an APR of 8%, compounded monthly. How much would your annual withdraw be? Do NOT round to less than three decimal places in the intermediate steps. Round your final answer to two decimal places.

Answer #1

The person will save for 42 years ranging from year 24th to 65th.

Interest rate = 6% per annum

Amount = $20,000

FV factor @6% for 42 period = 175.95

Thus the Future Value of savings at the end of 65th year will be = 20,000*175.95 = $ 3,519,010.89

Interest rate earned on this balance @8% APR. i.e EAR would be (1+8%/12)^12 = 8.30%

Pension withdrawal period would be 66th year to 99th year = 34 installments

PV factor @8.3% for 34 years = 11.25

Therefore, annual amount that can be withdrawn would be $3,519,110.89 / 11.25 = $312,875.03

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