You want to buy a car, and a local bank will lend you $35,000. The loan would be fully amortized over 3 years (36 months), and the nominal interest rate would be 15%, with interest paid monthly. What is the monthly loan payment? Do not round intermediate calculations. Round your answer to the nearest cent. 

To calculate the monthly loan payment, we will use the formula for a fully amortized loan, which is:

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

Where:
- $PMT$ is the monthly payment,
- $P$ is the loan amount (\$35,000),
- $r$ is the monthly interest rate (annual nominal rate divided by 12),
- $n$ is the total number of payments (36 months).

### Step-by-step calculation:

1. **Loan amount $P$** = \$35,000
2. **Nominal annual interest rate** = 15%
3. **Monthly interest rate $r$** = $ \frac{15\%}{12} = 0.0125$
4. **Number of payments $n$** = 36 months (3 years)

Now, we plug these values into the formula:

\[
PMT = \frac{35000 \cdot 0.0125 \cdot (1 + 0.0125)^{36}}{(1 + 0.0125)^{36} - 1}
\]

Let me calculate that for you.The monthly loan payment is approximately **$1,213.29**.

Would you like any further details or clarifications on this?

Here are some related questions to expand your understanding:

1. How does the interest rate affect the monthly payment?
2. What would happen to the monthly payment if the loan term were 5 years instead of 3 years?
3. How much total interest would be paid over the life of the loan?
4. What is the difference between nominal interest rate and effective interest rate?
5. How would a larger down payment impact your loan?

**Tip:** When taking out loans, always consider both the interest rate and loan term to find the best balance for your financial situation.

You want to buy a car, and a local bank will lend you $35,000. The loan would be fully amortized over 3 years (36 months), and the nominal interest rate would be 15%, with interest paid monthly. What is the monthly loan payment? Do not round intermediate calculations. Round your answer to the nearest cent.

Learn how to calculate the monthly payment for a $35,000 car loan with a 15% annual interest rate amortized over 36 months. This example includes the loan amortization formula and step-by-step calculations. Suitable for advanced high school and college-level students.

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