Question

A sum of money becomes Rs.9680 at 10% simple interest per annum in 4 years. The principal amount is:

• A. Rs.6800.35
• B. Rs.6914.28
• C. Rs.7000.97
• D. Rs.7200.27

Hint:

Think in terms of percentages! At $10%$ per year for 4 years, the total simple interest earned is $10% \times 4 = 40%$. Therefore, the total accumulated amount represents $100% \text{ (Principal)} + 40% \text{ (Interest)} = 140%$ of the principal. $$140% \text{ of } P = 9680 \implies P = \frac{9680}{14} \approx \text{Rs.}6914.28$$

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In simple interest calculations, the interest earned each year remains constant because it is calculated only on the initial principal amount ($P$). The total accumulated amount ($A$) at the end of a given timeframe is the sum of the original principal amount and the total simple interest ($SI$) accumulated across those years.

Step 2: Key Formula or Approach:
1. $\text{Simple Interest (SI)} = \frac{P \times R \times T}{100}$ 2. $\text{Total Amount (A)} = P + SI = P \left(1 + \frac{R \times T}{100}\right)$ Where $P = \text{Principal}$, $R = \text{Rate of interest per annum}$, and $T = \text{Time in years}$.

Step 3: Detailed Explanation:
Given values from the problem statement: Accumulated Amount ($A$) = Rs.9680 Rate of interest ($R$) = $10%$ per annum Time duration ($T$) = 4 years Substitute these values into the total amount equation: $$9680 = P \left(1 + \frac{10 \times 4}{100}\right)$$ $$9680 = P \left(1 + \frac{40}{100}\right)$$ $$9680 = P \left(1 + 0.4\right) = 1.4P$$ Isolate the Principal variable ($P$) by dividing 9680 by 1.4: $$P = \frac{9680}{1.4} = \frac{96800}{14}$$ Let's divide 96800 by 14 step-by-step: $$P = \frac{96800}{14} = 6914.28...$$

Step 4: Final Answer:
The principal amount is Rs.6914.28.