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?

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.