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