on a certain principal, simple interest amounts to Rs. 2,000 in two years ai the rate of 10% p.a. What will be the difference in the amount of interest if the same is compounded on annual basis?

Options

A. Rs. 200
B. Rs. 220
C. Rs. 100
D. Rs. 120

Answer

To solve the problem, we need to calculate both the Simple Interest (SI) and the Compound Interest (CI) for the given principal amount, and then find the difference between them.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Simple Interest (SI) = Rs. 2000
- Time (T) = 2 years
- Rate of Interest (R) = 10% per annum

2. **Calculate the Principal using Simple Interest Formula:**
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Rearranging the formula to find the Principal (P):
\[ P = \frac{SI \times 100}{R \times T} \]
Substituting the known values:
\[ P = \frac{2000 \times 100}{10 \times 2} = \frac{200000}{20} = 10000 \]
So, the Principal (P) is Rs. 10,000.

3. **Calculate the Compound Interest for 2 Years:**
The formula for Compound Interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where A is the total amount after time T.
Substituting the values:
\[ A = 10000 \left(1 + \frac{10}{100}\right)^2 = 10000 \left(1 + 0.1\right)^2 = 10000 \left(1.1\right)^2 \]
Calculating \( (1.1)^2 \):
\[ (1.1)^2 = 1.21 \]
Now, substituting back:
\[ A = 10000 \times 1.21 = 12100 \]

4. **Calculate the Compound Interest (CI):**
Compound Interest (CI) is given by:
\[ CI = A - P \]
Substituting the values:
\[ CI = 12100 - 10000 = 2100 \]

5. **Find the Difference between CI and SI:**
Now, we need to find the difference between the Compound Interest and the Simple Interest:
\[ \text{Difference} = CI - SI = 2100 - 2000 = 100 \]

### Final Answer:
The difference in the amount of interest if the same is compounded on an annual basis is **Rs. 100**.