Ashley bought a new car for $31,000. She paid a 10 % down payment and financed the remaining balance for 48 months with an APR of  4.1%. Assuming she made monthly payments determine the total cost of Ashley's Round your answer to the nearest cent if necessary

To calculate the total cost of Ashley's car, we will follow these steps:

### **Step 1: Calculate the down payment**
The car's total price is $31,000, and Ashley made a 10% down payment.

\[
\text{Down payment} = 31,000 \times 0.10 = 3,100
\]

### **Step 2: Determine the financed amount**
The remaining amount to be financed is the total price minus the down payment:

\[
\text{Financed amount} = 31,000 - 3,100 = 27,900
\]

### **Step 3: Monthly interest rate and number of payments**
The loan is financed over 48 months with an APR of 4.1%. First, we need to convert the APR to a monthly interest rate.

\[
\text{Monthly interest rate} = \frac{4.1\%}{12} = \frac{0.041}{12} \approx 0.00341667
\]

The total number of payments (months) is 48.

### **Step 4: Calculate the monthly payment**
The formula for the monthly payment $M$ on a loan is:

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

where:
- $ P $ is the principal loan amount = 27,900
- $ r $ is the monthly interest rate ≈ 0.00341667
- $ n $ is the number of payments = 48

Let's calculate the monthly payment.The monthly payment amount is approximately $631.20.

### **Step 5: Calculate the total cost of the loan**
The total cost of the loan over the 48 months is:

\[
\text{Total cost of loan} = 631.20 \times 48
\]

Let's calculate that.The total cost of the loan over 48 months is approximately $30,297.83.

### **Step 6: Calculate the total cost of the car**
The total cost of the car includes the down payment plus the total cost of the loan:

\[
\text{Total cost of the car} = 3,100 + 30,297.83 = 33,397.83
\]

Therefore, the total cost of Ashley's car is approximately **$33,397.83**.

Would you like more details or have any questions?

### Related Questions
1. How much interest did Ashley pay over the 48 months?
2. What would be the monthly payment if the APR were reduced to 3%?
3. How much would Ashley save if she financed over 36 months instead of 48 months?
4. What would be the impact of a 20% down payment instead of 10%?
5. How does changing the loan term to 60 months affect the monthly payment?

**Tip:** Always check the APR rates offered by different lenders, as even small changes in the rate can significantly impact the total cost of the loan.

Ashley bought a new car for $31,000. She paid a 10% down payment and financed the remaining balance for 48 months with an APR of 4.1%. Assuming she made monthly payments, determine the total cost of Ashley's car. Round your answer to the nearest cent if necessary.

Learn how to calculate the total cost of a car purchase, including monthly payments and loan amortization. Ashley's car was bought for $31,000 with a 10% down payment and a 4.1% APR. Follow the detailed steps to determine the total cost over 48 months. Suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation