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 receive 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?

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Rigoberto

20 February, 23:31

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 receive 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?

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Rachael Benjamin · Answer 1

Answer: $34,696

Explanation: $1000,000/25=$40,000 as deposit to be made 25 times, but out of this amount 8% interest will be subtracted which gives 8/100*40,000=$3200.

Hence annual deposit will be $40000-$3200=$36800.

But annual raise of 3% should be subtracted as well making deposit to be 3/100*36800=$1104.

Substracting we have $36800-$1104=$35696.

Hence i must deposit $35696 first to meet this goal.