You want to buy a car.  A dealership in town has a car you like for $32,000.  Your first financing option is to make a down payment of $2000 and finance the rest at 8.9% APR for 60 months.
How much will you be financing?  $

How much will your monthly payments be under this financing option?  (Round to the nearest cent.)  $

How much total money will you pay for this car at the end of the 60 months under this financing option?  (Don't forget to include your down payment in this total amount.)
$

Let's break this down step by step.

### 1. **How much will you be financing?**

To find the amount you will be financing, subtract the down payment from the price of the car:

\[
\text{Amount to be financed} = \text{Car Price} - \text{Down Payment}
\]

\[
\text{Amount to be financed} = 32,000 - 2,000 = 30,000
\]

So, you will be financing **$30,000**.

### 2. **How much will your monthly payments be under this financing option?**

To calculate the monthly payment for an auto loan, we use the formula for the monthly payment of a loan:

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

Where:
- $M$ = monthly payment
- $P$ = loan amount (principal) = $30,000
- $r$ = monthly interest rate = $\frac{\text{APR}}{12} = \frac{8.9\%}{12} = 0.007417$
- $n$ = number of payments = 60 months

Now, let's calculate the monthly payment.

\[
M = \frac{30,000 \times 0.007417 \times (1 + 0.007417)^{60}}{(1 + 0.007417)^{60} - 1}
\]

I will now calculate this.The monthly payment under this financing option is approximately **$621.30**.

### 3. **How much total money will you pay for this car at the end of the 60 months?**

To find the total payment, we need to calculate the total of all monthly payments over the loan period and add the down payment:

\[
\text{Total Payments} = M \times n + \text{Down Payment}
\]

Where:
- $M = 621.30$
- $n = 60$ months
- Down payment = $2,000

Let's calculate this total.The total amount you will pay for the car at the end of the 60 months, including the down payment, is approximately **$39,277.74**.

### Summary:
1. Amount to be financed: **$30,000**
2. Monthly payment: **$621.30**
3. Total amount paid for the car: **$39,277.74**

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. What if the interest rate was lower? How would it affect your payments?
2. What would be the impact of a larger down payment on your loan?
3. How does changing the loan term (e.g., 48 or 72 months) affect the total cost?
4. Can you pay off the loan early, and how would that affect the total cost?
5. How does the APR of 8.9% compare with other typical car loans?

**Tip:** Always check if there are any early repayment penalties before deciding to pay off your loan sooner!

You want to buy a car. A dealership in town has a car you like for $32,000. Your first financing option is to make a down payment of $2000 and finance the rest at 8.9% APR for 60 months. How much will you be financing? How much will your monthly payments be under this financing option? How much total money will you pay for this car at the end of the 60 months under this financing option?

Calculate how much you will finance, your monthly payment, and the total amount paid for a $32,000 car with a $2,000 down payment at 8.9% APR over 60 months. This problem covers loan calculations, interest rates, and total cost analysis, suitable for Grades 9-12.

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