Explain how you reached the answer or show your work if a mathematical calculati

Question

Explain how you reached the answer or show your work if a mathematical calculation is needed, or both. 3. Riverside Bank offers to lend you $50,000 at a nominal rate of 6.5%, compounded monthly. The loan (principal plus interest) must be repaid at the end of the year. Midwest Bank also offers to lend you the $50,000, but it will charge an annual rate of 7.0%, with no interest due until the end of the year. How much higher or lower is the effective annual rate charged by Midwest versus the rate charged by Riverside? a. 0.52% b. 0.44% c. 0.36% d. 0.30% e. 0.24%

Explanation / Answer

According to the given information,

Nominal return for Riverside = 6.5%

Nominal return for Midwest = 7.0%

Periods for Riverside = 12

Periods for Midwest = 1

This problem can be worked using the conversion formula. The formula is shown below:

Effective interest rate (Riverside) = {[1+ (rnom / N)]^N} - 1

                                                   = {[ 1 + (0.065 / 12)]^ 12}- 1)

                                                   = {[ 1 + 0.00542] ^ 12} - 1

                                                   = 1.0670 - 1

                                                   = 0.067 or 6.7%

Therefore, the effective interest rate is 6.7% for Riverside

But the effective interest rate for Mid west is 7.0%

The difference is (7.0% - 6.7%) = 0.3%

Therefore, the correct option is d) 0.30%

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