Joanie takes a $\$6,\!000$ 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

$16.32

Explanation:

The applicable formula for compound interest is as below.

FV = PV × (1+r)n

Fv is future value

PV  present value : $6000

r interest rate : 4% or 0.04

n: number of compounds

IF compounded annually

FV = 6000 x (1 +0.04)4

FV = 6000 X 1.1698585

FV =7, 019.15

IF compounded quarterly

FV = 6000 x (1+0.04/4)4*4

FV = 6000 x (1+0.01)16

Fv = 6000 x 1.172578

Fv = 7, 035.47

The difference between quarterly and annual compounding

= $7, 035.47 - $7, 019.15

=$16.32

answer; a large down payment,a longer term loan, would result in a lower monthly payment;

24 years, i believe is the correct answer.