Question

The difference between the CI and the SI on a sum of money lent for 2 years at 20% interest per annum is 80. The sum is:

• A. ₹2,000
• B. ₹1,200
• C. ₹1,500
• D. ₹1,000

Hint:

For 2 years, the difference between CI and SI is simply the "interest on the first year's interest."
Interest for 1st year = $20\% \text{ of } P$.
Difference = $20\% \text{ of } (20\% \text{ of } P) = 80$.
$0.04P = 80 \implies P = 2000$.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Compound Interest (CI) is interest calculated on the principal and the accumulated interest of previous periods. Simple Interest (SI) is calculated only on the principal. For the first year, CI and SI are the same, but they diverge from the second year onwards.

Step 2: Key Formula or Approach:
For a period of 2 years, the difference ($D$) between CI and SI is given by the formula: \[ D = P \left( \frac{R}{100} \right)^2 \] Where: $P$ = Principal (Sum), $R$ = Rate of interest per annum.

Step 3: Detailed Explanation:
Given: Difference ($D$) = 80 Rate ($R$) = 20% Time ($T$) = 2 years Substituting the values into the formula: \[ 80 = P \left( \frac{20}{100} \right)^2 \] \[ 80 = P \left( \frac{1}{5} \right)^2 \] \[ 80 = P \left( \frac{1}{25} \right) \] \[ P = 80 \times 25 \] \[ P = 2000 \]

Step 4: Final Answer:
The sum of money (Principal) is ₹2,000.