Find the approximate annual percentage rate using the approximate annual percentage rate formula. Round to the nearest tenth of a percent.

Amount financed: $403
Finance charge: $50
Number of monthly payments: 18
Select one:

A.
12.4%

B.
15.7%

C.
17.5%

D.
9.8%

To find the approximate annual percentage rate (APR), we use the following formula:

\[
\text{APR} \approx \frac{2 \times \text{Finance Charge} \times 12}{\text{Amount Financed} \times (\text{Number of Monthly Payments} + 1)}
\]

Given:
- Amount financed ($ P $) = $403
- Finance charge ($ F $) = $50
- Number of monthly payments ($ n $) = 18

Plugging these values into the formula:

\[
\text{APR} \approx \frac{2 \times 50 \times 12}{403 \times (18 + 1)}
\]

First, calculate the denominator:

\[
403 \times (18 + 1) = 403 \times 19 = 7657
\]

Then, calculate the numerator:

\[
2 \times 50 \times 12 = 1200
\]

Now, divide the numerator by the denominator:

\[
\frac{1200}{7657} \approx 0.1567
\]

Convert this decimal to a percentage by multiplying by 100:

\[
0.1567 \times 100 = 15.67\%
\]

Rounding to the nearest tenth of a percent, the APR is approximately 15.7%.

Thus, the correct answer is:

**B. 15.7%**

Would you like more details or have any questions about this calculation?

Here are some related questions:
1. What is the formula for calculating the exact APR?
2. How does the finance charge affect the APR?
3. What is the difference between APR and interest rate?
4. How does the number of payments affect the APR?
5. Can the APR be lower than the interest rate? If so, how?
6. What is the impact of rounding on the APR calculation?
7. How would the APR change if the amount financed was different but the finance charge remained the same?
8. What are some practical applications of understanding the APR in personal finance?

**Tip:** When comparing loans, always consider the APR along with the interest rate to understand the true cost of borrowing.

Learn how to calculate the approximate annual percentage rate (APR) for a loan using the given finance charge, amount financed, and number of monthly payments. This problem covers finance concepts such as APR calculation and percentage calculations, rounded to the nearest tenth of a percent. Suitable for advanced learners and professionals.

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