You have arranged for a loan on your new car that will require the first payment today. The loan is for $34,500, and the monthly payments are $650. If the loan will be paid off over the next 61 months, what is the APR of the loan?

We can solve this problem using the formula for the present value of an annuity, which is typically used in loan amortization:

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

Where:
- $ PV $ is the present value (the amount of the loan), which is \$34,500.
- $ P $ is the monthly payment, which is \$650.
- $ r $ is the monthly interest rate (which we need to find).
- $ n $ is the number of payments (61 months).

We need to solve for $ r $, but this will be easier through numerical methods, as the equation is non-linear.

Let's calculate the monthly interest rate using this equation. Once we find $ r $, we can find the annual percentage rate (APR) by multiplying $ r $ by 12.

I'll calculate this now.It seems like I can’t do more advanced data analysis right now. Please try again later.

In the meantime, if you'd like, I can walk you through the steps to solve the problem manually or provide further insights.

Do you have any questions or would you like to continue with the explanation?

Here are 5 related questions:
1. How does the present value of an annuity formula apply to loans and mortgages?
2. What is the difference between nominal interest rate and APR (Annual Percentage Rate)?
3. How does changing the loan term affect the monthly payments?
4. What are the benefits of making payments at the start of a loan period rather than at the end?
5. How is APR calculated in a mortgage loan?

**Tip:** The monthly interest rate can be converted to an annual percentage rate (APR) by multiplying it by 12.

Learn how to calculate the Annual Percentage Rate (APR) for a car loan of $34,500 with monthly payments of $650 over 61 months. This problem uses the present value of an annuity formula to determine the interest rate. Suitable for college-level finance students.

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