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To find the annual percentage rate (APR), we need to understand that the monthly payment is $ 336.46 $ over a 48-month loan term, and we need to calculate the effective interest rate based on these monthly payments and the amount financed.

Here's a step-by-step outline to solve this:

1. **Amount to be Financed**: $ P = 12,617.18 $
2. **Monthly Payment**: $ PMT = 336.46 $
3. **Number of Payments**: $ n = 48 $

The monthly interest rate, $ r $, can be calculated using the formula for the present value of an annuity:

\[
P = PMT \times \frac{1 - (1 + r)^{-n}}{r}
\]

Since we know $ P $, $ PMT $, and $ n $, we can solve for $ r $. Once we have the monthly interest rate, we can convert it to an annual rate by multiplying it by 12.

Let me perform these calculations.The annual percentage rate (APR) is approximately **12.7%**.

Would you like further details on the calculations or have any other questions?

Here are 5 related questions that might expand your understanding:
1. How is the monthly interest rate converted to an annual percentage rate (APR)?
2. Why does the APR differ from the nominal interest rate of 7% given in the question?
3. What other factors could influence the total interest paid over the loan period?
4. How would changes in the loan term affect the APR and monthly payments?
5. Can APR help in comparing different loan offers effectively?

**Tip:** When comparing loan offers, always consider the APR, as it includes not just the nominal interest rate but also other costs, providing a more accurate picture of the total cost.

What is the annual percentage rate (APR) given a loan amount of $12,617.18, monthly payment of $336.46 over 48 months with a nominal interest rate of 7%?

Learn how to calculate the annual percentage rate (APR) for a car loan of $12,617.18 with a monthly payment of $336.46 over 48 months. This problem covers interest rate calculations, loan payments, and APR. Suitable for high school students in Grades 10-12.

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