Let's break down the problem and calculate the finance charge and the annual percentage rate (APR) step by step.

We are given:

• Amount Financed = $18,200
• Number of Payments = 72
• Monthly Payment = $424.08

1. Total Amount Paid Over the Loan

The total amount paid over the life of the loan is calculated by multiplying the monthly payment by the number of payments.

$\text{Total Amount Paid} = \text{Monthly Payment} \times \text{Number of Payments}$

$\text{Total Amount Paid} = 424.08 \times 72 = 30,533.76$

2. Finance Charge

The finance charge is the difference between the total amount paid and the amount financed.

$\text{Finance Charge} = \text{Total Amount Paid} - \text{Amount Financed}$

$\text{Finance Charge} = 30,533.76 - 18,200 = 12,333.76$

So, the finance charge is $12,333.76.

3. APR Calculation

To calculate the APR, we will use the following formula for an approximate APR for installment loans:

$\text{APR} \approx \frac{2 \times N \times F}{P \times (T + 1)}$

Where:

• $N$ = number of payments per year (usually 12)
• $F$ = finance charge ($12,333.76)
• $P$ = amount financed ($18,200)
• $T$ = total number of payments (72)

Let's now plug in the values:

$\text{APR} \approx \frac{2 \times 12 \times 12,333.76}{18,200 \times (72 + 1)}$

We can calculate this next.The APR (Annual Percentage Rate) is approximately 22.3%.

Summary:

• Finance Charge: $12,333.76
• APR: 22.3%

Would you like more details or have any questions?

Here are five related questions for further exploration:

1. How does the APR change if the monthly payment is reduced?
2. What is the impact of shortening the loan term on the APR?
3. How does the finance charge differ between fixed and variable APR loans?
4. What methods can be used to lower the total finance charge?
5. How does the APR formula differ from the effective annual rate (EAR) calculation?

Tip: The APR is a useful tool for comparing loans, as it accounts for both interest and additional costs.