You want to buy a $21,000 car. The company is offering a 3% interest rate for 36 months (3 years). What will your monthly payments be? round to the nearest cent.

To determine the monthly payments for a $21,000 car loan with a 3% annual interest rate over 36 months, we can use the formula for the monthly payment on an installment loan:

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

where:
- $ PMT $ is the monthly payment
- $ P $ is the principal loan amount ($21,000)
- $ r $ is the monthly interest rate (annual rate divided by 12)
- $ n $ is the number of monthly payments

First, we need to convert the annual interest rate to a monthly rate:
\[ r = \frac{3\%}{12} = \frac{0.03}{12} = 0.0025 \]

The number of monthly payments is:
\[ n = 36 \]

Now we can plug these values into the formula:

\[ PMT = \frac{21000 \times 0.0025 \times (1 + 0.0025)^{36}}{(1 + 0.0025)^{36} - 1} \]

First, calculate $(1 + 0.0025)^{36}$:

\[ (1 + 0.0025)^{36} = 1.0025^{36} \approx 1.093443 \]

Now plug this back into the formula:

\[ PMT = \frac{21000 \times 0.0025 \times 1.093443}{1.093443 - 1} \]
\[ PMT = \frac{21000 \times 0.0025 \times 1.093443}{0.093443} \]
\[ PMT = \frac{21000 \times 0.0025 \times 1.093443}{0.093443} \]
\[ PMT = \frac{57.048575}{0.093443} \]
\[ PMT \approx 610.42 \]

So, your monthly payments will be approximately $610.42.

Would you like further details or have any questions?

Here are some related questions you might consider:
1. How does the loan term affect the monthly payment amount?
2. What would the monthly payment be with a different interest rate?
3. How much total interest will be paid over the life of the loan?
4. What are the advantages of making a larger down payment on the car?
5. How can I calculate the remaining balance on a loan after a certain number of payments?

**Tip:** When taking out a loan, it's important to consider the total cost of borrowing, which includes the interest paid over the life of the loan. This helps you understand the true cost of your purchase.

Learn how to calculate monthly car loan payments for a $21,000 car with a 3% interest rate over 36 months. Get a detailed step-by-step solution using the installment loan payment formula. Understand the total cost of borrowing and the impact of interest rates on monthly payments.

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