DeShawn bought a car for $24,000 three years ago. The loan had a 5 year term at 3% interest rate. How much does he still owe on the car?

To determine how much DeShawn still owes on the car, we need to calculate the remaining balance on the loan after 3 years.

This is a case of an **amortized loan** where DeShawn is making monthly payments over 5 years (60 months) at an interest rate of 3% per year. Let's follow these steps:

### Step 1: Calculate the Monthly Interest Rate
\[
\text{Monthly interest rate} = \frac{3\%}{12} = 0.25\% \text{ per month} = \frac{0.03}{12} = 0.0025
\]

### Step 2: Determine the Loan's Total Number of Payments
\[
\text{Total number of payments} = 5 \text{ years} \times 12 = 60 \text{ months}
\]

### Step 3: Calculate the Monthly Payment Using the Amortization Formula
The formula for the monthly payment is:
\[
M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}
\]
Where:
- $M$ = Monthly payment
- $P$ = Principal loan amount = $24,000
- $r$ = Monthly interest rate = 0.0025
- $n$ = Total number of payments = 60

### Step 4: Calculate the Remaining Balance After 3 Years
To find out how much is left after 3 years (36 months), we will need to compute the balance remaining after making 36 payments.

I will calculate this for you.DeShawn's monthly payment is approximately **$431.25**.

After making 36 payments (3 years), DeShawn still owes about **$11,654.99** on the car.

Would you like a detailed breakdown of how these calculations were done, or do you have any specific questions?

Here are some related questions for deeper exploration:

1. How much interest has DeShawn paid over the first 3 years?
2. What would happen if DeShawn made an extra payment each month?
3. How would the loan terms change if the interest rate increased to 4%?
4. How much would DeShawn owe if the loan term was 7 years instead of 5?
5. What would DeShawn’s monthly payments be if the loan had no interest?

**Tip:** Making additional payments towards the principal reduces the overall interest paid and shortens the loan term.

DeShawn bought a car for $24,000 three years ago. The loan had a 5-year term at a 3% interest rate. How much does he still owe on the car?

Discover how to calculate the remaining balance on a $24,000 car loan after 3 years with a 5-year term and 3% interest rate. This amortization problem involves calculating monthly payments and determining the balance using standard loan formulas. Suitable for high school students studying algebra and financial mathematics.

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