Explanation: To understand the difference between Compound Interest (CI) and Simple Interest (SI) on a principal amount for a period of 2 years, we need to first understand the formulas for both CI and SI.
Simple Interest (SI) is calculated using the formula:
\[ SI = \frac{P \times R \times T}{100} \]
where \( P \) is the principal amount, \( R \) is the rate of interest per annum, and \( T \) is the time period in years.
Compound Interest (CI) is calculated using the formula:
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]
where \( P \) is the principal amount, \( R \) is the rate of interest per annum, and \( T \) is the time period in years.
For a period of 2 years, the difference between CI and SI can be calculated using a simplified formula:
\[ \text{Difference} = P \left(\frac{R}{100}\right)^2 \]
Given:
- Principal amount (\( P \)) = Rs 200
- Rate of interest (\( R \)) = 10% p.a
- Time period (\( T \)) = 2 years
Using the simplified formula for the difference:
\[ \text{Difference} = 200 \left(\frac{10}{100}\right)^2 \]
\[ \text{Difference} = 200 \left(\frac{1}{10}\right)^2 \]
\[ \text{Difference} = 200 \times \frac{1}{100} \]
\[ \text{Difference} = 2 \]
Therefore, the difference between CI and SI on Rs 200 at 10% p.a for 2 years is Rs 2.
This formula is particularly useful in competitive exams where time is a critical factor, as it allows for quick calculations without having to compute the CI and SI separately. It is important to remember this formula and understand its derivation to avoid common mistakes in calculations.