The simple interest at 10% p.a. on a deposit for 2 years is Rs 4,000. If the interest in compounded on an annual basis, how much more will be the amount of interest ?

Options

A. Rs 200
B. Rs 240
C. Rs 220
D. Rs 190

Answer

To solve the problem step by step, we need to find the principal amount first using the given simple interest, and then calculate the compound interest to find out how much more it is compared to the simple interest.

### Step 1: Calculate the Principal Amount
We know that the formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \(SI\) = Simple Interest (Rs 4,000)
- \(P\) = Principal amount (unknown)
- \(R\) = Rate of interest (10%)
- \(T\) = Time (2 years)

Substituting the known values into the formula:
\[ 4000 = \frac{P \times 10 \times 2}{100} \]
This simplifies to:
\[ 4000 = \frac{20P}{100} \]
\[ 4000 = \frac{P}{5} \]
Multiplying both sides by 5 gives:
\[ P = 4000 \times 5 = 20000 \]

### Step 2: Calculate the Compound Interest
The formula for Compound Interest (CI) is:
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]
Substituting the values we have:
\[ CI = 20000 \left(1 + \frac{10}{100}\right)^2 - 20000 \]
This simplifies to:
\[ CI = 20000 \left(1 + 0.1\right)^2 - 20000 \]
\[ CI = 20000 \left(1.1\right)^2 - 20000 \]
Calculating \( (1.1)^2 \):
\[ (1.1)^2 = 1.21 \]
Now substituting back:
\[ CI = 20000 \times 1.21 - 20000 \]
\[ CI = 24200 - 20000 = 4200 \]

### Step 3: Calculate the Difference Between CI and SI
Now we need to find out how much more the compound interest is compared to the simple interest:
\[ \text{Difference} = CI - SI \]
Substituting the values:
\[ \text{Difference} = 4200 - 4000 = 200 \]

### Final Answer
The amount of interest that is more when compounded annually compared to simple interest is Rs 200.