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

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 you goal? (8 points)

Solutions

Expert Solution

Sol:

Future value (FV) = $1,000,000

Period (n) = 25 years

Interest rate (r) = 8%

Growth rate (g) = 3%

To determine how much must your first deposit (PMT) be if you are to meet you goal:

FV of a Growing Annuity Due = PMT x [(1 + r)^n - (1 + g)^n / (r - g)] x (1 + r)

1,000,000 = PMT x [(1 + 8%)^25 - (1 + 3%)^25 / (8% - 3%)] x (1 + 8%)

1,000,000 = PMT x [(1.08)^25 - (1.03)^25 / (0.08 - 0.03)] x (1 + 0.08)

1,000,000 = PMT x [6.848475 - 2.093778 / (0.05)] x (1.08)

1,000,000 = PMT x [4.754697 / 0.05] x (1.08)

1,000,000 = PMT x (95.09394 x 1.08)

1,000,000 = PMT x 102.701455

PMT = 1,000,000 /102.701455 = $9736.96

Therefore your first deposit is if you are to meet you goal will be $9736.96

jeff jeffy answered 2 years ago

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