First Simple Bank pays 9.4 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 9 years?

Problem 6-29 Simple Interest versus Compound Interest [LO4]

First Simple Bank pays 9.4 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 9 years? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer

 

Explanation

The total interest paid by First Simple Bank is the interest rate per period times the number of periods. In other words, the interest by First Simple Bank paid over 9 years will be:

.0940(9) = .846

First Complex Bank pays compound interest, so the interest paid by this bank will be the FV factor of $1 minus the initial investment of $1, or:

(1 + r)9 − 1

Setting the two equal, we get:

.0940(9) = (1 + r)9 − 1

r = 1.8461/9 − 1

r = .0705, or 7.05%