You wish to accumulate $1 million by your retirement date, which is 25 years fro

Question

You wish to accumulate $1 million 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 9.92% 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

So we have FVga = PMT*[{(1+r)^n - (1+g)^n}/(r-g)]*(1+i) where PMT =First annual payment r = Int rate g = growth rate in PMT n = no of periods (1+i) at end of eqn = This is Annuity Due case = payemnt is made at start of period So we have $1M = PMT*[{(1+9.92%)^25 - (1+2%)^25}/(9.92%-2%)]*(1+9.92%) So PMT = $1,000,000/124.8926 = $8006.8767

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