Question

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. 0.35% B. 0.50% C. 0.30% D. 0.45%

Answer 1

Riverside Bank

Effective annual rate is calculated using the below formula:

EAR= (1+r/n)^n-1

Where r is the interest rate and n is the number of compounding periods in one year.

EAR= (1 + 0.065/12)^12 – 1

        = 1.0670 – 1

        = 0.0670*100

        = 6.70%

Midwest Bank

Effective annual rate is calculated using the below formula:

EAR= (1+r/n)^n-1

Where r is the interest rate and n is the number of compounding periods in one year.

EAR= (1 + 0.07/1)^1 – 1

        = 1.07 -1

        = 0.07*100

        = 7.00%

=7.00% - 6.70%

= 0.30%

Therefore, the effective annual rate charged by Midwest Bank is 0.30% higher than the one charged by Riverside Bank.

Hence, the answer is option c.

In case of any query, kindly comment on the solution.