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Time Value of Money and Investments

You are currently 30 years of age. You intend to retire at age 60 and you want to be able to receive a 20-year, $100,000 beginning-of-year annuity with the first payment to be received on your 60th birthday. You would like to save enough money over the next 15 years to achieve your objective; that is, you want to accumulate the necessary funds by your 45th birthday.

a. If you expect your investments to earn 12 percent per year over the next 15 years and 10 percent per year thereafter, how much must you accumulate by the time you reach age 45?

b. What equal, annual amount must you save at the end of each of the next 15 years to achieve your objective, assuming that you currently have $10,000 available to meet your goal? Assume the conditions stated in Part a.

Solution Preview

a. We first find the present value of the amount that you need at your 60th birthday. You need to be able to get 100,000 a year for 20 years annuity at the beginning of the period. The interest rate applicable will be 10%. We use the PVIFA table to get the PV amount. For 20 years and 10%, the factor is 8.514. The amount needed is 100,000X8.514=851,400. ...

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