Suppose you are now 25 years old and just accepted a job offer. You would like...

Suppose you are now 25 years old and just accepted a job offer. You would like to save for retirement, but not sure how much you must set aside. Your new employer offers a retirement plan that provides 5% return per year. The plan does not allow withdrawals before the age of 62. You plan to retire at the age 62. You expect that your life expectancy is 80 years. You believe that that you will need $110,000 per year, starting at the end of the first year in retirement and ending on your 80th birthday. You plan to contribute the same amount at the end of each year while you work. What is the amount of your annual contributions to achieve your retirement income need?

Expert Solution

Amount required at the age of 62 = Present value of future withdrawals

= 110,000*PVAF(5%, 18 years)

= 110,000*11.6896

= $1,285,856

Let amount required to be saved each year be x

Future value of annuity = Annual amount*[{(1+r)^n - 1}/r]

1,285,856 = x*[{(1.05)^37 - 1}/0.05]

1,285,856 = 101.6281x

x= $12,652.56

Hence, amount required to be saved each year = $12,652.56

jeff jeffy answered 2 years ago

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