The simple interest accrued on an amount of ₹20.000 at the end of three years is ₹7.200. What would be the compound interest accrued on the same amount at the same rate in the same period?

Options

A. ₹8098.56
B. ₹8246.16
C. ₹8112.86
D. ₹8342.36

Explanation

To solve the problem of finding the compound interest accrued on an amount of ₹20,000 at the same rate and time period as the simple interest, we will follow these steps:

### Step 1: Identify the given values
- Principal (P) = ₹20,000
- Simple Interest (SI) = ₹7,200
- Time (T) = 3 years

### Step 2: Calculate the Rate of Interest (R)
Using the formula for simple interest:
\[ SI = \frac{P \times R \times T}{100} \]
We can rearrange this to find the rate of interest (R):
\[ R = \frac{SI \times 100}{P \times T} \]
Substituting the known values:
\[ R = \frac{7200 \times 100}{20000 \times 3} \]
Calculating this:
\[ R = \frac{720000}{60000} = 12\% \]

### Step 3: Calculate the Compound Interest (CI)
The formula for the amount (A) in compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Substituting the values we have:
\[ A = 20000 \left(1 + \frac{12}{100}\right)^3 \]
This simplifies to:
\[ A = 20000 \left(1.12\right)^3 \]

### Step 4: Calculate \((1.12)^3\)
Calculating \(1.12^3\):
\[ 1.12^3 = 1.404928 \]
Now, substituting this back into the amount formula:
\[ A = 20000 \times 1.404928 \approx 28098.56 \]

### Step 5: Calculate the Compound Interest (CI)
The compound interest is given by:
\[ CI = A - P \]
Substituting the values:
\[ CI = 28098.56 - 20000 \approx 8098.56 \]

### Final Answer
The compound interest accrued on the same amount at the same rate in the same period is approximately **₹8098.56**.

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