A sum of `Rs. 6000` becomes `Rs. 7200` in 2 years, when invested in a scheme of simple interest. If the same sum is invested in a scheme of compound interest with same yearly interest rate (compounding of Interest is done yearly), then what will be the amount (in Rs.) after 3 years?

Options

A. 7434
B. 8244
C. 7864
D. 7986

Answer

To solve the problem step by step, we need to first find the interest rate from the simple interest scenario and then use that rate to calculate the amount in the compound interest scenario.

### Step 1: Calculate the Simple Interest
We know that:
- Principal (P) = Rs. 6000
- Amount (A) after 2 years = Rs. 7200
- Time (T) = 2 years

The formula for Simple Interest (SI) is:
\[ \text{SI} = A - P \]

Substituting the values:
\[ \text{SI} = 7200 - 6000 = 1200 \]

### Step 2: Calculate the Rate of Interest
Using the formula for Simple Interest:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where R is the rate of interest.

Substituting the known values:
\[ 1200 = \frac{6000 \times R \times 2}{100} \]

Rearranging the equation to find R:
\[ 1200 = \frac{12000R}{100} \]
\[ 1200 = 120R \]
\[ R = \frac{1200}{120} = 10\% \]

### Step 3: Calculate the Amount in Compound Interest
Now that we have the rate of interest (R = 10%), we can calculate the amount after 3 years using the formula for Compound Interest (CI):
\[ A = P \left(1 + \frac{R}{100}\right)^T \]

Substituting the values:
\[ A = 6000 \left(1 + \frac{10}{100}\right)^3 \]
\[ A = 6000 \left(1 + 0.1\right)^3 \]
\[ A = 6000 \left(1.1\right)^3 \]

Calculating \( (1.1)^3 \):
\[ (1.1)^3 = 1.331 \]

Now substituting back:
\[ A = 6000 \times 1.331 \]
\[ A = 7986 \]

### Final Answer
The amount after 3 years when invested in a scheme of compound interest is Rs. 7986.

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