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To solve the problem, we need to calculate the maturity value of the car loan using the **simple interest formula**:

\[
I = P \cdot r \cdot t
\]

Where:
- $ I $ is the simple interest,
- $ P $ is the principal loan amount (here, $ P = 7,000 $),
- $ r $ is the annual interest rate as a decimal (here, $ r = 7.9\% = 0.079 $),
- $ t $ is the time in years (since $ t = 15 $ months, we convert it to years as $ t = \frac{15}{12} = 1.25 $).

Once we calculate the simple interest $ I $, the maturity value is given by:

\[
\text{Maturity Value} = P + I
\]

### Step-by-step Calculation:
1. **Convert Interest Rate to Decimal**:
   $ r = 7.9\% = 0.079 $.

2. **Convert Time to Years**:
   $ t = \frac{15}{12} = 1.25 \text{ years} $.

3. **Find the Simple Interest**:
   \[
   I = P \cdot r \cdot t = 7,000 \times 0.079 \times 1.25
   \]

Let me calculate that.The simple interest $ I $ is \$691.25.

### Step 4: Calculate the Maturity Value
Now, the maturity value is the sum of the principal and the interest:

\[
\text{Maturity Value} = P + I = 7,000 + 691.25 = 7,691.25
\]

So, the maturity value of the car loan is **\$7,691.25**.

Would you like further details on any part of the process, or do you have any additional questions?

Here are 5 related questions for further exploration:
1. How would the maturity value change if the interest rate were 10%?
2. What if the loan term were extended to 24 months? How would that affect the interest?
3. Can you derive the formula for the maturity value if compounded interest is used instead of simple interest?
4. How would a partial loan repayment halfway through the term affect the interest calculation?
5. How does the simple interest formula differ from the formula used for compound interest?

**Tip:** Always remember to convert months to years when calculating time in simple interest problems.

A credit union loans a member $7,000 for the purchase of a used car. The loan is made for 15 months at an annual simple interest rate of 7.9%. What is the maturity value of the car loan?

Learn how to calculate the maturity value of a $7,000 car loan at an annual simple interest rate of 7.9% over 15 months. This solution covers simple interest formulas and step-by-step calculations, making it suitable for high school students (Grades 9-12).

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