First Simple Bank pays 8.6 percent simple interest on its investment accounts. I

Question

First Simple Bank pays 8.6 percent simple interest on its investment accounts. If First Complex Bank pays interest on its accounts compounded annually, what rate should the bank set if it wants to match First Simple Bank over an investment horizon of 8 years? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

First Simple Bank pays 8.6 percent simple interest on its investment accounts. If First Complex Bank pays interest on its accounts compounded annually, what rate should the bank set if it wants to match First Simple Bank over an investment horizon of 8 years? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Explanation / Answer

1) Let the principal amount investment in First Simple Bank be $100.

The time horizon is 8 years and the interest rate is 8.6%(simple interest rate)

Interest earned per year on the investment = $8.6

Interest earned over 8 years = $68.80

After 8 years the value of the investment will be: $100 (Principal) + $68.80(Interest) = $168.80.

2) Now, for the First Complex Bank, $100 invested for 8 years should have $168.80 as the FV.

Hence, solving for I/Y(interest rate) using the formula: FV = PV * (1 + I/Y)N

$168.80 = $100 * (1 + I/Y)8

1.6880 = (1 + I/Y)8

I/Y = 6.76% is the compound interest rate First Complex Bank should set to match the FV of the First Simple Bank.

I hope my solution solves your query.

Regards.

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