You want to buy a $23,000 car. You can make a 10% down payment, and will finance the balance with a 5% interest rate for 36 months (3 years). What will your monthly payments be?


To determine the monthly payments for financing the car, we will use the formula for calculating monthly payments on a loan:

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

Where:
- $ M $ is the monthly payment.
- $ P $ is the loan principal (amount to be financed after the down payment).
- $ r $ is the monthly interest rate (annual rate divided by 12).
- $ n $ is the total number of payments (number of months).

### Step 1: Calculate the down payment and loan amount
The down payment is 10% of $23,000:

\[
\text{Down payment} = 0.10 \times 23,000 = 2,300
\]

So, the loan amount to be financed is:

\[
P = 23,000 - 2,300 = 20,700
\]

### Step 2: Determine the monthly interest rate and total number of payments
The annual interest rate is 5%, so the monthly interest rate is:

\[
r = \frac{5\%}{12} = \frac{0.05}{12} = 0.004167
\]

The loan is for 36 months (3 years), so:

\[
n = 36
\]

### Step 3: Calculate the monthly payment
Now, we can plug the values into the formula:

\[
M = \frac{20,700 \cdot 0.004167 \cdot (1 + 0.004167)^{36}}{(1 + 0.004167)^{36} - 1}
\]

I'll calculate that for you.The monthly payment for the car loan will be approximately **$620.40**.

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

Here are 5 related questions to explore:

1. How much total interest will you pay over the life of the loan?
2. What would the monthly payments be if the loan term was extended to 48 months?
3. How does the down payment affect the monthly payment?
4. What would happen if the interest rate increased to 6%?
5. What is the total cost of the car, including interest, by the end of the loan?

**Tip:** Always consider the total cost of the loan, including interest, when financing a large purchase like a car.

You want to buy a $23,000 car. You can make a 10% down payment, and will finance the balance with a 5% interest rate for 36 months (3 years). What will your monthly payments be?

Find out how to calculate the monthly payments for a $23,000 car loan with a 10% down payment and a 5% interest rate over 36 months. This step-by-step guide uses the loan amortization formula and covers key financial math concepts.

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