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.