You are interested in a car which costs $25,000. You have a $2000 down payment, and  you have found a 4-year loan at 4.5% annual interest compounded monthly. How much  total interest do you end up paying if you make equal monthly payments over the entire  four years? 

To calculate the total interest paid on a car loan with equal monthly payments, we need to follow these steps:

### 1. **Calculate the Loan Amount**
The loan amount is the car price minus the down payment.

\[
\text{Loan Amount} = 25,000 - 2,000 = 23,000
\]

### 2. **Convert the Annual Interest Rate to Monthly Interest Rate**
The interest rate given is an annual rate of 4.5%, so we need to convert it to a monthly interest rate.

\[
\text{Monthly Interest Rate} = \frac{4.5\%}{12} = \frac{0.045}{12} = 0.00375
\]

### 3. **Determine the Number of Monthly Payments**
Since the loan term is 4 years, and payments are made monthly:

\[
\text{Number of Payments} = 4 \times 12 = 48
\]

### 4. **Use the Loan Payment Formula**
To calculate the monthly payment amount, we use the formula for a fixed-rate loan:

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

Where:
- $M$ = monthly payment
- $P$ = loan principal ($23,000)
- $r$ = monthly interest rate (0.00375)
- $n$ = total number of payments (48)

Let's calculate this.The monthly payment is approximately **$524.48**.

### 5. **Calculate the Total Amount Paid Over the Loan**
The total amount paid over the 4 years (48 months) is:

\[
\text{Total Paid} = 524.48 \times 48
\]

Let's calculate this.The total amount paid over the course of the loan is approximately **$25,175.05**.

### 6. **Calculate the Total Interest Paid**
The total interest paid is the difference between the total amount paid and the original loan amount:

\[
\text{Total Interest} = 25,175.05 - 23,000 = 2,175.05
\]

So, the total interest paid is approximately **$2,175.05**.

Would you like more details or have any questions?

Here are 5 follow-up questions:
1. What happens if you pay an extra $50 per month toward the principal?
2. How does a higher down payment affect the interest paid?
3. What if the interest rate were compounded quarterly instead of monthly?
4. How would extending the loan term to 5 years change the total interest?
5. What is the effect of making a lump sum payment halfway through the loan?

**Tip:** Always consider paying more than the required amount to reduce the total interest paid on a loan.

You are interested in a car which costs $25,000. You have a $2000 down payment, and you have found a 4-year loan at 4.5% annual interest compounded monthly. How much total interest do you end up paying if you make equal monthly payments over the entire four years?

Learn how to calculate the total interest paid on a $23,000 car loan with 4.5% annual interest, compounded monthly over 4 years. This detailed solution walks through loan amortization, monthly payment formulas, and the final interest calculation. Ideal for students in Grades 10-12.

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