If the difference between the simple and the compound interest earned on a sum of money at the rate of 5% per annum for 2 yr is Rs 16, then find the principal.

Options

A. Rs 6200
B. Rs 6400
C. Rs 6250
D. Cannot be determined

Answer

To solve the problem, we need to find the principal amount given that the difference between the simple interest (SI) and compound interest (CI) for 2 years at a rate of 5% per annum is Rs 16.

### Step-by-Step Solution:

1. **Understand the Formulas:**
- The formula for Simple Interest (SI) for 2 years is:
\[ SI = \frac{P \times R \times T}{100} \]
- The formula for Compound Interest (CI) for 2 years is:
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]

2. **Calculate SI for 2 Years:**
- Here, \( R = 5\% \) and \( T = 2 \) years.
- Therefore, the formula for SI becomes:
\[ SI = \frac{P \times 5 \times 2}{100} = \frac{10P}{100} = \frac{P}{10} \]

3. **Calculate CI for 2 Years:**
- The CI can be calculated as follows:
\[ CI = P \left(1 + \frac{5}{100}\right)^2 - P = P \left(1.05^2\right) - P \]
- Calculating \( 1.05^2 \):
\[ 1.05^2 = 1.1025 \]
- Thus,
\[ CI = P \times 1.1025 - P = 0.1025P \]

4. **Find the Difference Between CI and SI:**
- The difference between CI and SI is given as:
\[ CI - SI = 0.1025P - \frac{P}{10} \]
- Converting \( \frac{P}{10} \) to a decimal:
\[ \frac{P}{10} = 0.1P \]
- Therefore, the difference becomes:
\[ 0.1025P - 0.1P = 0.0025P \]

5. **Set Up the Equation:**
- We know from the problem that this difference equals Rs 16:
\[ 0.0025P = 16 \]

6. **Solve for Principal (P):**
- To find \( P \), divide both sides by 0.0025:
\[ P = \frac{16}{0.0025} = 6400 \]

### Final Answer:
The principal amount is Rs 6400.