Question

Farmers Bank offers to lend you $50,000 at a nominal rate of 5.0%, simple interest, with interest paid quarterly. Merchants Bank offers to lend you the $50,000, but it will charge 6.0%, simple interest, with interest paid at the end of the year. What's the difference in the effective annual rates charged by the two banks? a. 1.56% b. 1.30% c. 0.72% d. 0.91% e. 1.09%

Answer 1

Answer: d. 0.91%

Explanation:

Farmers Bank

Effective annual rate is calculated with the formula:

= (1 + Rate / number of compounding period in a year) ^ number of compounding periods in a year - 1

= ( 1 + 5%/4 quarters) ⁴ - 1

= 5.09%

Merchants bank's rate is already an annual figure so there is no need for conversion.

Difference is:

= 6% - 5.09%

= 0.91%