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

Question

You want 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 8% interest, compounded annually. you expect to get annual raises of 3%, which will offset inflation, and you will let the amount you deposit each year also grow by 3% (i.e., your second deposit will be 3% greater than your first, the third will be 3% greater than the second, etc.) How much must your first deposit be if you are to meet your goal?

Explanation / Answer

We need to use FV of a Growing Annuity Due concept 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+8%)^25 - (1+3%)^25}/(8%-3%)]*(1+8%) is $1M = PMT*{4.7547/5%}*1.08 = 102.70*PMT So PMT = $1,000,000/102.70 = $9736.96 SO ANnual payment of $9736.96 growing at Rate of 3% & invested at 8% will result in $1M at end of 25 years.

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