Joanie takes a $6000 loan to pay for her car. The annual 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?

The amount due under quarterly compounding is higher by =$ 187.12

Explanation:

To determine the amount  money  by which the quarterly compunding is greater, we would compare the total sum due under the two compounding options.

This is done below:

Quarterly compounding

FV = A × (1+r)^n

PV - principal  amount owed = 6,000

r- quarterly interest rate = 12%/4 = 3% per three month

n - number of quarters in 4 years = 4× 4 = 16

Loan amount due with interest after 4 years

= 6,000× (1.03)^(48) = 9628.23

Annual compounding

PV - principal  amount owed = 6,000

r- annual interest rate = 12% =

n - number of  years = 4  

Loan amount due =6,000× (1.12)^(4) =  9,441.12

The amount due under quarterly compounding is higher by

= 9628.23 - 9,441.12

=$ 187.12

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