Suppose you borrow $8,500 at 8.75% interest for 10 months. What are the
interest and the maturity value?
Interest = _______________
Maturity value = _______________

To calculate both the interest and the maturity value of the loan, we will use the simple interest formula:

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

Where:
- $ I $ = Interest
- $ P $ = Principal (amount borrowed) = \$8,500
- $ r $ = Interest rate = 8.75% (or 0.0875 as a decimal)
- $ t $ = Time in years = 10 months (which is $ \frac{10}{12} $ years)

### Step 1: Calculate the Interest
\[
I = 8,500 \times 0.0875 \times \frac{10}{12} 
\]
\[
I = 8,500 \times 0.0875 \times 0.8333 
\]
\[
I = 619.79
\]

So, the interest is **$619.79**.

### Step 2: Calculate the Maturity Value
The maturity value is the total amount to be paid at the end of the loan period, which is the principal plus the interest:

\[
\text{Maturity value} = P + I = 8,500 + 619.79 = 9,119.79
\]

So, the maturity value is **$9,119.79**.

### Final Answer:
- **Interest** = \$619.79
- **Maturity value** = \$9,119.79

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. How would the interest change if the loan period were 12 months instead of 10 months?
2. What would the interest be if the interest rate were 10% instead of 8.75%?
3. How can the compound interest formula be applied if the interest were compounded monthly?
4. How much more would you owe if you extended the loan period by 2 more months?
5. How would the maturity value change if the interest rate dropped to 7%?

**Tip:** Always convert time into years when using the simple interest formula. 

Suppose you borrow $8,500 at 8.75% interest for 10 months. What are the interest and the maturity value?

Learn how to calculate the simple interest and maturity value for an $8,500 loan at 8.75% interest over 10 months. Using the simple interest formula, this solution breaks down the steps to find the interest ($619.79) and maturity value ($9,119.79). Suitable for Grades 8-10.

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