ind simple interest and total amount of ₹ 8250 at the \( r \) \( 6 \% \) per annum for \( 3 \frac{1}{2} \) years.

To calculate the simple interest (SI) and the total amount (A) for a principal amount (P) of ₹ 8250 at an interest rate (r) of 6% per annum for a time period (t) of \( 3 \frac{1}{2} \) years, we can use the following formulas: 1. **Simple Interest (SI)**: \[ SI = \frac{P \times r \times t}{100} \] 2. **Total Amount (A)**: \[ A = P + SI \] ### Step 1: Convert the time period First, convert \( 3 \frac{1}{2} \) years into a decimal: \[ 3 \frac{1}{2} = 3 + \frac{1}{2} = 3.5 \text{ years} \] ### Step 2: Calculate Simple Interest Now, substitute the values into the SI formula: - \( P = 8250 \) - \( r = 6 \) - \( t = 3.5 \) \[ SI = \frac{8250 \times 6 \times 3.5}{100} \] Calculating the above: \[ SI = \frac{8250 \times 6 \times 3.5}{100} = \frac{173250}{100} = 1732.50 \] ### Step 3: Calculate Total Amount Now, calculate the total amount using the formula: \[ A = P + SI \] \[ A = 8250 + 1732.50 = 9982.50 \] ### Final Results - **Simple Interest (SI)**: ₹ 1732.50 - **Total Amount (A)**: ₹ 9982.50