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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?

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Answer:

effective annual rate charged by Midwest versus the rate charged by Riverside is 0.3%

Explanation:

given data:

Nominal return for Riverside = 6.5%

Nominal return for Midwest = 7.0%

Periods for Riverside = 12

Periods for Midwest = 1

By using the conversion formula.

Effective interest rate (Riverside) =[tex]{[1+ (\frac{r_{nom}}{N})]^N} - 1[/tex]

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

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

                                                    = 1.0670 - 1

Effective interest rate (Riverside) = 0.067 or 6.7%

but nominal rate of interest for Mid west is 7.0%

therefore

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

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