Calculate the finance charge (in $) and the annual percentage rate for the installment loan by using the APR formula. (Round dollar amounts to the nearest cent and percentages to one decimal place.)
Amount
Financed	Number of
Payments	Monthly
Payment	Finance
Charge	APR
$18,200	72	$424.08	$
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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.

Calculate the finance charge (in $) and the annual percentage rate for the installment loan by using the APR formula. (Round dollar amounts to the nearest cent and percentages to one decimal place.) Amount Financed: $18,200, Number of Payments: 72, Monthly Payment: $424.08.

Learn how to calculate the finance charge and annual percentage rate (APR) for a $18,200 installment loan over 72 payments with a monthly payment of $424.08. This guide walks you through step-by-step calculations for finance charges and APR using essential finance formulas. Ideal for students in Grades 11-12 or college-level finance courses.

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