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?

Question

Business

Vaughn

3 June, 08:40

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?

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Anabel Waller · Answer 1

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%