https://file.aiquickdraw.com/mathbot/file/17269678918824anrfutb.jpg

The problem in the image asks to calculate the total cost of Lindsey's car purchase after financing. Here's how we can solve it:

1. **Initial Car Price:** $29,000
2. **Down Payment:** 10% of $29,000 = $ 0.10 \times 29000 = 2900 $
3. **Amount Financed:** The remaining balance to be financed is $ 29,000 - 2,900 = 26,100 $.
4. **Interest Rate (APR):** 4.5% annual, which means the monthly interest rate $ r = \frac{4.5\%}{12} = 0.00375 $.
5. **Loan Duration:** 36 months.

### Monthly Payment Calculation

The formula for the monthly payment on a loan with a fixed interest rate is given by:

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

Where:
- $ M $ = monthly payment
- $ P $ = loan principal ($26,100)
- $ r $ = monthly interest rate (0.00375)
- $ n $ = number of payments (36 months)

Let's calculate that now.Lindsey's monthly payment will be approximately **$776.39**.

To calculate the total cost of the car:
- Total amount paid over the loan period = $ 776.39 \times 36 = 27,950.21 $.

### Total Cost:
- Down payment: $2,900
- Total payments for the loan: $27,950.21

Thus, the total cost of Lindsey's car is approximately **$30,850.21**.

Would you like any further details or clarifications?

Here are five related questions:
1. What would the monthly payment be if the loan term was 48 months instead of 36?
2. How does the APR affect the total cost of financing?
3. What would be the total cost if the interest rate increased to 6% APR?
4. How much interest does Lindsey pay over the course of the loan?
5. What if Lindsey paid an additional amount towards the principal each month?

**Tip:** Making extra payments on a loan can significantly reduce the total interest paid.

Lindsey bought a new car for $29,000. She paid a 10% down payment and financed the remaining balance for 36 months with an APR of 4.5%. Determine the total cost of Lindsey’s car.

Calculate the total cost of a car loan with a $29,000 price, a 10% down payment, and financing for 36 months at 4.5% APR. Learn step-by-step how to compute monthly payments and the overall car cost, including interest.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation