A car dealership offers a loan with 3.8% interest for 36 months, and you plan to purchase a car for $17,500. You can afford a down payment of $3,500.

(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 break down the solution for each part:

### Known values:
- **Loan amount (after down payment)**: $17,500 - $3,500 = $14,000
- **Interest rate**: 3.8% per year (annual percentage rate or APR)
- **Loan term**: 36 months (3 years)

We will use the following formula to calculate the monthly payment:

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

Where:
- $M$ = monthly payment
- $P$ = loan amount = $14,000
- $r$ = monthly interest rate = $\frac{3.8\%}{12}$ per month
- $n$ = number of months = 36 months

Let's solve each part step-by-step:

### (a) Monthly payment

I will first calculate the monthly payment.### (a) The monthly payment is approximately **$412.09**.

Now, let's calculate the total amount paid over the life of the loan.

\[
\text{Total amount paid} = M \times n
\] 

Where:
- $ M = 412.09 $
- $ n = 36 $

I'll calculate the total next.### (b) The total amount you will pay for the car over the life of the loan is approximately **$14,835.29**.

Next, we will calculate the total interest paid:

\[
\text{Total interest paid} = \text{Total amount paid} - \text{Loan amount}
\]

I'll calculate the interest next.### (c) The total interest paid over the life of the loan is approximately **$835.29**.

Let me know if you need any more details or have any questions!

Here are 5 related questions to expand on this topic:

1. How would the monthly payment change if the loan term was extended to 48 months?
2. What would be the total interest paid if the interest rate increased to 5%?
3. How much would the total payment be if the down payment increased to $5,000?
4. How would bi-weekly payments affect the overall interest paid on the loan?
5. What is the effective interest rate if compounded monthly instead of annually?

**Tip:** A longer loan term results in lower monthly payments, but you'll end up paying more interest overall.

A car dealership offers a loan with 3.8% interest for 36 months, and you plan to purchase a car for $17,500. You can afford a down payment of $3,500. (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?

Learn how to calculate the monthly payments, total cost, and interest for a car loan with a 3.8% interest rate over 36 months, given a purchase price of $17,500 and a $3,500 down payment. This detailed breakdown covers key concepts in loan amortization and interest rate calculations.

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