Question

The difference between the compound interest, compounded annually, and the simple interest earned on a certain sum of money in two years at 10% interest per annum, is ₹197.2. Find the sum invested.

• A. ₹19,720
• B. ₹17,720
• C. ₹16,720
• D. ₹18,720

Answer 1

Answer:

A. ₹19,720

The sum invested is ₹19,720.

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For a time period of 2 years, the mathematical relationship between Compound Interest ($CI$) and Simple Interest ($SI$) is represented by the following direct formula:

$\text{Difference } (CI - SI) = P \times \left(\frac{R}{100}\right)^2$

Where:

• $P$ = Principal sum invested

• $R$ = Rate of interest per annum = 10%

• $\text{Difference}$ = ₹197.2

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Detailed Calculation

1. Substitute the given values into the formula:
   $197.2 = P \times \left(\frac{10}{100}\right)^2$

2. Simplify the fraction inside the square:
   $197.2 = P \times \left(\frac{1}{10}\right)^2$
   $197.2 = P \times \frac{1}{100}$

3. Solve for the Principal ($P$):
   $P = 197.2 \times 100$
   $P = 19720$