https://file.aiquickdraw.com/mathbot/file/17303488709870o82yos7.jpg

To solve this problem, we'll use the formula for simple interest:

\[
\text{Simple Interest} = \frac{P \times R \times T}{100}
\]

where:
- $ P $ is the principal amount (initial loan),
- $ R $ is the rate of interest per year, and
- $ T $ is the time period in years.

Given values:
- **Principal (P)** = $2850
- **Rate (R)** = 7.5%
- **Time (T)** = $ 2 \frac{1}{2} $ years, which we convert to $ 2.5 $ years for calculation.

### Step-by-Step Calculation

1. Substitute the values into the formula:
   \[
   \text{Simple Interest} = \frac{2850 \times 7.5 \times 2.5}{100}
   \]

2. Calculate the multiplication inside the numerator:
   \[
   2850 \times 7.5 \times 2.5 = 53343.75
   \]

3. Now, divide by 100 to get the interest:
   \[
   \text{Simple Interest} = \frac{53343.75}{100} = 533.4375
   \]

### Answer
The simple interest owed for the loan is approximately **$533.44** (when rounded to two decimal places).

Would you like further details or have any questions?

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### Related Questions
1. What would the interest be if the time were 3 years instead of $2 \frac{1}{2}$ years?
2. How does changing the interest rate to 8% affect the total interest owed?
3. What is the formula for compound interest, and how would it change the interest calculation?
4. If the principal amount were increased to $3000, what would the new simple interest be?
5. What is the total amount owed after including the interest?

### Tip
Remember, simple interest grows linearly with time, unlike compound interest, which grows exponentially.

Find the simple interest owed for the following loan:
Principal: $2850, Rate: 7.5%, Time in Years: 2 1/2

Learn how to calculate the simple interest owed on a $2850 loan with a 7.5% interest rate over a period of 2.5 years. This problem covers essential concepts in simple interest calculation, percentage, and fractional time conversion. Suitable for Grades 7-9.

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