Philip buys a new car, where he makes $500 down payment and finances the remaining balance at the interest rate of 15% compounded monthly. The loan will be amortized (paid back) with 60 monthly payments of $260 each
What is the total interest paid?

To calculate the total interest paid on the car loan, we need to determine the total amount paid over the loan period and subtract the initial principal amount borrowed from this total.

Here are the steps:

### 1. Calculate the total amount paid over the 60 months:
Each monthly payment is $260, and the total number of payments is 60.

\[
\text{Total Payments} = 260 \times 60 = 15,600
\]

### 2. Calculate the amount of the loan (Principal):
Philip made a $500 down payment, so the amount financed (the principal) is the car's price minus the down payment. However, the car's price is not given directly. We can infer it by using the fact that the loan was fully financed for 60 months at an interest rate of 15% compounded monthly. 

We can use the **loan amortization formula** to find the principal:

\[
P = \frac{A}{\left( \frac{r(1+r)^n}{(1+r)^n - 1} \right)}
\]

Where:
- $P$ is the principal (amount borrowed)
- $A = 260$ is the monthly payment
- $r = \frac{0.15}{12} = 0.0125$ is the monthly interest rate
- $n = 60$ is the total number of monthly payments

Let's compute $P$.The principal (amount borrowed) is approximately \$10,929.

### 3. Calculate the total interest paid:
The total amount paid over 60 months is \$15,600, and the principal amount borrowed is approximately \$10,929.

The total interest paid is:

\[
\text{Total Interest} = \text{Total Payments} - \text{Principal} = 15,600 - 10,929 = 4,671
\]

Thus, the total interest paid is approximately **\$4,671**.

Would you like further details or have any questions?

Here are five related questions to expand on this:
1. How would the total interest change if the interest rate was 10% instead of 15%?
2. What would the monthly payment be if the loan was repaid over 48 months instead of 60?
3. How does the length of the loan term affect the total interest paid?
4. How would the total interest change if the loan was compounded quarterly instead of monthly?
5. How can extra monthly payments reduce the total interest paid on a loan?

**Tip:** Making additional payments on your loan (even small ones) can significantly reduce the total interest paid over time.

Philip buys a new car, where he makes $500 down payment and finances the remaining balance at the interest rate of 15% compounded monthly. The loan will be amortized (paid back) with 60 monthly payments of $260 each. What is the total interest paid?

Learn how to calculate the total interest paid on a car loan with a 15% monthly compounded interest rate, a $500 down payment, and 60 monthly payments of $260. This solution includes detailed steps using loan amortization formulas. Suitable for high school students in Grades 10-12.

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