A person invests Rs.10,000 at the rate of 10% per annum for 2 years on simple interest. How much more interest will be earned if he is paid compound interest instead of simple interest, interest being compounded annually?

Options

A. Rs.100
B. Rs.4100
C. Rs.2100
D. Rs 1

Answer

To solve the problem of how much more interest will be earned if the person is paid compound interest instead of simple interest, we will follow these steps:

### Step 1: Calculate Simple Interest (SI)
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount (Rs. 10,000)
- \( R \) = Rate of interest (10%)
- \( T \) = Time in years (2 years)

Substituting the values:
\[ SI = \frac{10000 \times 10 \times 2}{100} = \frac{200000}{100} = 2000 \]

### Step 2: Calculate Compound Interest (CI)
The formula for Compound Interest is:
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]
Where:
- \( P \) = Principal amount (Rs. 10,000)
- \( R \) = Rate of interest (10%)
- \( T \) = Time in years (2 years)

Substituting the values:
\[ CI = 10000 \left(1 + \frac{10}{100}\right)^2 - 10000 \]
\[ = 10000 \left(1 + 0.1\right)^2 - 10000 \]
\[ = 10000 \left(1.1\right)^2 - 10000 \]
\[ = 10000 \times 1.21 - 10000 \]
\[ = 12100 - 10000 = 2100 \]

### Step 3: Calculate the Difference in Interest
Now, we will find the difference between the Compound Interest and Simple Interest:
\[ \text{Difference} = CI - SI \]
Substituting the values:
\[ \text{Difference} = 2100 - 2000 = 100 \]

### Conclusion
The amount of more interest earned if he is paid compound interest instead of simple interest is **Rs. 100**.

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