If in 3 years at simple interest the principal increases by 15%. What will be the approximate compound interest earned (in Rs lakhs) on Rs 15 lakhs in 3 years at the same rate?

Options

A. 7.81
B. 2.87
C. 2.36
D. 3.38

Answer

To solve the problem, we need to follow these steps:

### Step 1: Determine the Rate of Interest
Given that the principal increases by 15% in 3 years at simple interest, we can find the rate of interest.

Let the principal amount (P) be Rs 100 (for simplicity). The increase in 3 years is 15% of Rs 100, which is Rs 15.

Using the formula for simple interest:
\[ \text{Simple Interest} = \frac{P \times r \times t}{100} \]
where:
- \( P = 100 \)
- \( r \) is the rate of interest
- \( t = 3 \) years

We can set up the equation:
\[ 15 = \frac{100 \times r \times 3}{100} \]
This simplifies to:
\[ 15 = 3r \]
Thus, solving for \( r \):
\[ r = \frac{15}{3} = 5\% \]

### Step 2: Calculate Compound Interest
Now that we know the rate of interest is 5%, we can calculate the compound interest on Rs 15 lakhs over 3 years.

The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^t \]
where:
- \( P = 15 \) lakhs
- \( r = 5 \)
- \( t = 3 \)

Substituting the values:
\[ A = 15 \left(1 + \frac{5}{100}\right)^3 \]
This simplifies to:
\[ A = 15 \left(1 + 0.05\right)^3 = 15 \left(1.05\right)^3 \]

### Step 3: Calculate \( (1.05)^3 \)
Calculating \( (1.05)^3 \):
\[ (1.05)^3 = 1.157625 \]
Thus:
\[ A = 15 \times 1.157625 \approx 17.364375 \text{ lakhs} \]

### Step 4: Calculate Compound Interest Earned
The compound interest (CI) is given by:
\[ CI = A - P \]
Substituting the values:
\[ CI = 17.364375 - 15 = 2.364375 \text{ lakhs} \]

### Step 5: Approximate the Compound Interest
Rounding off the compound interest:
\[ CI \approx 2.36 \text{ lakhs} \]

### Final Answer
The approximate compound interest earned on Rs 15 lakhs in 3 years at the same rate is **Rs 2.36 lakhs**.

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