A sum of `Rs. 3000` amounts to `Rs. 6000` in two years at compound interest. The interest for four years is :

Options

A. ` Rs. 9000`
B. `Rs. 12000 `
C. `Rs. 6000 `
D. `Rs. 3000`

Answer

To solve the problem step by step, we will follow the concept of compound interest.

### Step 1: Understand the given information
We know that:
- Principal (P) = Rs. 3000
- Amount after 2 years (A) = Rs. 6000

### Step 2: Calculate the interest earned in 2 years
The interest earned over the 2 years can be calculated using the formula:
\[ \text{Interest} = \text{Amount} - \text{Principal} \]
Substituting the values:
\[ \text{Interest} = 6000 - 3000 = 3000 \]

### Step 3: Determine the interest earned in the first 2 years
Since the amount doubles from Rs. 3000 to Rs. 6000 in 2 years, the interest earned in these 2 years is Rs. 3000.

### Step 4: Calculate the amount after 4 years
Since the interest is compounded, the amount after the next 2 years will also double again. Therefore, the amount after 4 years will be:
\[ \text{Amount after 4 years} = 6000 + 3000 = 12000 \]

### Step 5: Calculate the total interest for 4 years
Now, we can find the total interest earned over the 4 years:
\[ \text{Total Interest} = \text{Amount after 4 years} - \text{Principal} \]
Substituting the values:
\[ \text{Total Interest} = 12000 - 3000 = 9000 \]

### Final Answer
The interest for four years is Rs. 9000.

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