Harry decided to save money for his new born son’s college cost right now. He wa

Question

Harry decided to save money for his new born son’s college cost right now. He wants to have $120,000 in 18 years. Bank of America has a program paying 2.5% interest rate compounded monthly. Harry has two options. Option A, deposit a big amount of money now and withdraw it after 18 years. Option B, deposit a small amount of money at the end of every month for 18 years. (a) For option A, how much does he need to deposit now? (b) How much total interest will he receive for option A? (c) For option B, what is his monthly payment? (d) How much total interest will he receive for option B?

Explanation / Answer

For option A:

Using compound interest formula:

A = P*(1 + i/n)^(n*t)

P = A/(1 + i/n)^(n*t)

using given values:

P = 120000/(1 + 0.025/12)^(12*18)

P = 76551.2034

He needs to deposit $76551.34

B.

Interest earned = 120000 - 76551.34 = $43448.66

C.

If he decides to deposit periodic payment, then

FV = PMT*[(1 + i)^nt - 1]/(i/n)

PMT = FV*(i/n)/[(1 + i/n)^(nt) - 1]

Using given values:

PMT = 120000*(0.025/12)/[(1 + 0.025/12)^(12*18) - 1]

PMT = $440.46 per month

monthly payment = $440.46

D.

Total amount invested = $440.46*12*18 = $95139.36

Interest earned = 120000 - 95139.36 = $24860.64

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