Question

The simple interest on a sum for 3 years at 8% per annum is ₹720. The principal amount is:

• A. ₹2500
• B. ₹3000
• C. ₹3200
• D. ₹3500

Hint:

Think in terms of net percentage! If you earn 8% interest every year for 3 years, your total simple interest earned is $8\% \times 3 = 24\%$ of the principal. Given that $24\% = \text{₹}720$, then $1\% = \frac{720}{24} = \text{₹}30$. Since the full principal is always $100\%$, then $100\% = 30 \times 100 = \text{₹}3000$.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Simple interest calculation accumulates a fixed percentage of the initial borrowed or invested sum (the principal) over regular intervals. Since the interest rate is constant and only applies to the principal, the interest earned remains identical every year.

Step 2: Key Formula or Approach:
The standard simple interest formula is written as: $$\text{SI} = \frac{P \times R \times T}{100}$$ Rearranging the formula to isolate the Principal ($P$): $$P = \frac{\text{SI} \times 100}{R \times T}$$ Where: $\text{SI} = \text{₹}720$ (Simple Interest) $T = 3 \text{ years}$ (Time period) $R = 8\% \text{ per annum}$ (Rate of interest)

Step 3: Detailed Explanation:
Substitute the given values into the rearranged equation to find the Principal amount: \[ P = \frac{720 \times 100}{8 \times 3} \] Simplify the denominator product: \[ 8 \times 3 = 24 \] \[ P = \frac{720 \times 100}{24} \] Now divide 720 by 24 (since $24 \times 3 = 72$, then $720 / 24 = 30$): \[ P = 30 \times 100 = \text{₹}3000 \]

Step 4: Final Answer:
The initial principal amount is ₹3000.