A car dealership offers a loan with 6% interest for 48 months, and you plan to purchase a car for $17,000. You can afford a down payment of $2,000.

(a) What will your monthly payment be? $

(b) How much will you pay in total for the car? $

(c) How much will you pay in interest over the life of the loan? $

Let's go through each part of the problem step-by-step:

### Step 1: Determine the Loan Amount

Since you can afford a down payment of $2,000, the amount you need to borrow for the loan is:

\[
\text{Loan Amount} = \text{Car Price} - \text{Down Payment} = 17,000 - 2,000 = 15,000
\]

### Step 2: Find the Monthly Payment

We will use the formula for calculating the monthly payment of a loan:

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

Where:
- $M$ is the monthly payment,
- $P$ is the loan amount,
- $r$ is the monthly interest rate (annual interest rate divided by 12),
- $n$ is the number of months.

Given:
- $P = 15,000$,
- The annual interest rate is 6%, so the monthly interest rate is $ \frac{6}{12} = 0.5\% = 0.005 $,
- The loan term is 48 months.

Now let's calculate the monthly payment.

\[
M = \frac{15000 \cdot 0.005 \cdot (1 + 0.005)^{48}}{(1 + 0.005)^{48} - 1}
\]

I'll calculate that next.(a) The monthly payment will be approximately **$352.28**.

### Step 3: Calculate the Total Payment

To find the total amount paid over the life of the loan, we multiply the monthly payment by the number of months:

\[
\text{Total Payment} = M \times n = 352.28 \times 48
\]

Let's calculate that.(b) The total amount you will pay for the car over the life of the loan is approximately **$16,909.22**.

### Step 4: Calculate the Total Interest Paid

To find the total interest paid, subtract the loan amount from the total payment:

\[
\text{Total Interest} = \text{Total Payment} - \text{Loan Amount} = 16,909.22 - 15,000
\]

Let's calculate the total interest.(c) The total amount you will pay in interest over the life of the loan is approximately **$1,909.22**.

### Summary:
- **(a)** Monthly payment: **$352.28**
- **(b)** Total payment: **$16,909.22**
- **(c)** Total interest: **$1,909.22**

Would you like more details on the calculations? Here are five related questions to explore further:

1. How would the monthly payment change if the loan term were 60 months instead of 48 months?
2. What would happen to the total interest paid if the interest rate were 5% instead of 6%?
3. How does the down payment affect the monthly payment and interest paid?
4. What is the formula for calculating the interest paid after a certain number of months?
5. How much would you save by increasing the down payment by $1,000?

**Tip:** Increasing your down payment reduces the loan principal, which in turn decreases both the monthly payments and total interest paid.

A car dealership offers a loan with 6% interest for 48 months, and you plan to purchase a car for $17,000. You can afford a down payment of $2,000.

(a) What will your monthly payment be? $
(b) How much will you pay in total for the car? $
(c) How much will you pay in interest over the life of the loan? $

Calculate your monthly car loan payment for a $17,000 vehicle with a 6% interest rate over 48 months. Learn how to determine your total payment and interest paid, using key formulas. Ideal for Grades 10-12 learners.

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