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 6.8%, 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?

Hello there!

Your answer would be 1.71%

Here is the work:

To find the annual paid interest for Farmer's Bank, since in the question it is the quarterly interest rate:

(1 + (0.05/4)) ^4 - 1 = 1.0125^4 - 1 = 0.0509 = 5.09%

Merchant's bank would be the same rate since it's already calculated as annually: 6.8%

Subtract those:

6.8-5.09 = 1.71%