MJSProblem 4-34 Growing Annuity Payments You want to accumulate $2 millions by y
ID: 2721483 • Letter: M
Question
MJSProblem 4-34
Growing Annuity Payments
You want to accumulate $2 millions by your retirement date, which is 25 years from now. You will make 25 deposits in your bank, with the first occurring today. The bank pays 6.78% interest, compounded annually. You expect to get an annual raise of 2%, which will offset inflation, and you will let the amount you deposit each year also grow by 2% (i.e., your second deposit will be 2% greater than your first, the third will be 2% greater than the second, etc.). How much must your first deposit be to meet your goal? Round your answer to the nearest cent.
Explanation / Answer
This is a classic example of calculating future value of growing annuity FV = P * [((1+r)^n - (1+g)^n] / (r-g) where P is initial investment g is growth rate of annuity r is rate of return n is tenure P = ? FV =$2m g = 2% r = 6.78% n = 25 2000000 = P * (1.0678^25 - 1.02^25) / (0.0678 - 0.02) or, 2000000 = P * (5.155228 - 1.640606) / 0.0478 or, 2000000 = P * 3.514622/0.0478 or, P = 2000000/73.52767 or, P = $27,200.65
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