you and a cars salesman ultimately decide on a sale price of 22,500$ for your new car. Your down payment is 3,500$. How much will your monthly payments be if you are financing at 5.75% compounded monthly for 3 years. What is the total cost of the car. How much will you end up paying in interest.

### 1. **Loan Amount Calculation:**

The total sale price of the car is $22,500, and your down payment is $3,500. Therefore, the loan amount (principal) is:

\[
\text{Loan Amount} = \text{Sale Price} - \text{Down Payment} = 22,500 - 3,500 = 19,000 \text{ dollars.}
\]

### 2. **Monthly Payment Calculation:**

We use the **loan amortization formula** to calculate the monthly payments:

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

Where:
- $M$ = monthly payment
- $P$ = loan amount = $19,000
- $r$ = monthly interest rate = $\frac{5.75\%}{12} = 0.00479$
- $n$ = total number of payments = $3 \times 12 = 36$ months

Let's calculate the monthly payment.

### 3. **Total Cost of the Car:**

The total cost of the car will be the sum of the down payment and the total of all monthly payments over the 3-year period.

\[
\text{Total Cost} = \text{Down Payment} + (M \times 36)
\]

### 4. **Total Interest Paid:**

The total interest paid will be the difference between the total cost and the original loan amount:

\[
\text{Interest} = \text{Total Cost} - \text{Loan Amount}
\]

Now, let's compute these values.### Results:
1. **Monthly Payment:** $575.87
2. **Total Cost of the Car:** $24,231.21
3. **Total Interest Paid:** $5,231.21

### Summary:
- Your monthly payment will be approximately **$575.87**.
- The total cost of the car (including down payment and all monthly payments) will be **$24,231.21**.
- You will end up paying **$5,231.21** in interest over the 3-year period.

Do you need further details or have any questions?

### Related Questions:
1. How does increasing the down payment affect the monthly payment?
2. What would be the impact if the loan term was extended to 5 years instead of 3?
3. How much would you save in interest with a 4.5% interest rate instead of 5.75%?
4. What would the total cost be if you made an additional payment of $500 every 6 months?
5. How does the monthly payment formula change if interest is compounded daily instead of monthly?

### Tip:
You can save on interest by paying off your loan faster or by making extra payments toward the principal!

You and a car salesman ultimately decide on a sale price of $22,500 for your new car. Your down payment is $3,500. How much will your monthly payments be if you are financing at 5.75% compounded monthly for 3 years? What is the total cost of the car? How much will you end up paying in interest?

Learn how to calculate monthly payments for a car priced at $22,500 with a down payment of $3,500, financed at 5.75% interest compounded monthly over 3 years. The solution includes key finance concepts like loan amortization, interest rate, and compound interest. Find out the total cost of the car and how much you'll pay in interest.

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