Question

Joanie takes a $6000 loan to pay for her car. The interest rate on the loan is 12%. She makes no payments for 4 years, but has to pay back all the money she owes at the end of 4 years. How much more money will she owe if the interest compounds quarterly than if the interest compounds annually?

I already figured out that if the interest compounds annually, she will pay $9441.12. The equation I used for that was:

(1.12)^4 (6000)

I am having trouble finding the equation that is similar to the one I showed above to figure out what would happen if the interest compounds quarterly. Please help if you can!

Thank you! :-)

Answer 1

the quarterly interest rate would be 12%/4 = 3%
but there are 16 quarters in 4 years.

so the amount would be 6000(1.03)^16 = 9628.24
which is $187.12 more than had it been compounded annually.