Christina bought a new car for $38,000
. She paid a 20%
 down payment and financed the remaining balance for 72
 months with an APR of 6.5%
. Determine the monthly payment that Christina pays. Round your answer to the nearest cent, if necessary.



Let's break down the problem step by step to find the monthly payment Christina has to make.

### Step 1: Calculate the Down Payment
Christina makes a **20% down payment** on the car, which costs $38,000.

\[
\text{Down Payment} = 38,000 \times 0.20 = 7,600
\]

### Step 2: Calculate the Amount to Be Financed
After making the down payment, Christina needs to finance the remaining balance.

\[
\text{Amount to be Financed} = 38,000 - 7,600 = 30,400
\]

### Step 3: Use the Loan Formula to Find Monthly Payment
The formula for the monthly payment on a loan is:

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

Where:
- $ M $ is the monthly payment.
- $ P $ is the loan principal (the amount financed).
- $ r $ is the monthly interest rate (APR divided by 12).
- $ n $ is the number of monthly payments.

In this case:
- $ P = 30,400 $
- Annual interest rate (APR) = 6.5% = 0.065
- Monthly interest rate $ r = \frac{0.065}{12} = 0.005417 $
- Loan term = 72 months

Now, plug the values into the formula to calculate $ M $:

\[
M = \frac{30,400 \times 0.005417(1 + 0.005417)^{72}}{(1 + 0.005417)^{72} - 1}
\]

Let me calculate that.The monthly payment Christina has to make is **$511.02**, rounded to the nearest cent.

Would you like further details or have any questions about this process?

Here are 5 related questions:
1. How would the payment change if the down payment was 15% instead of 20%?
2. What would be the impact of increasing the loan term to 84 months?
3. How much total interest will Christina pay over the life of the loan?
4. What if Christina could secure a 5% APR—how would her monthly payment change?
5. How does paying a higher down payment affect the total loan cost?

**Tip:** A lower APR or shorter loan term can significantly reduce the total interest paid over time.

Christina bought a new car for $38,000. She paid a 20% down payment and financed the remaining balance for 72 months with an APR of 6.5%. Determine the monthly payment that Christina pays. Round your answer to the nearest cent, if necessary.

Find out how to calculate Christina's monthly car payment for a $38,000 car purchase. Learn step-by-step how a 20% down payment and a 72-month loan with a 6.5% APR affect her monthly payment. This solution includes the loan amortization formula and down payment calculations. Suitable for high school students learning finance and algebra.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation