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Answer to Question #6020 in Economics of Enterprise for LaMarcus Streeter

Question #6020
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%
Expert's answer
d. 0.3% higher


Effective annual rate of Riverside Bank:
rR = (1 + (0.065/12))^12 = 1.067

Effective annual rate of Midwest Bank:
rM = (1 + (0.07/1))^1 = 1.07

effective annual rate of Midwest Bank is higher by (1.07 – 1.067) 0.003 or 0.3%

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