Question

Derek can deposit $237.00 per month for the next 10 years into an account at Bank A. The first deposit will be made next month. Bank A pays 14.00% and compounds interest monthly. Derek can deposit $2,417.00 per year for the next 10 years into an account at Bank B. The first deposit will be made next year. Bank B compounds interest annually. What rate must Bank B pay for Derek to have the same amount in both accounts after 10 years?

Answer #1

The question is solved in two parts. First, the future value of the deposits made in Bank A is calculated.

Information provided:

Monthly deposit= $237

Time= 10 years*12= 120 months

Interest rate= 14%/12= 1.1667% per month

Enter the below in a financial calculator to compute the future value.

PMT= -237

N= 120

I/Y= 1.1667

Press the CPT key and FV to compute the future value of annuity due.

The value obtained is 61,399.33.

Therefore, the future value of the deposits in Bank A is $61,399.33.

Next, the interest rate of Bank B is calculated by entering the below in a financial calculator:

FV= 61,399.33.

N= 10

PMT= -2,417

Press the CPT key and I/Y to compute the interest rate.

The value obtained is 19.5618.

Therefore, Bank B must offer a annual rate of return is 19.56%.

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