Ramu invested Rs. 12000 in a finance company at 10% per annum, interest is compounded annually for 3 years and Ravi invested Rs. 12000 for the same period at 15% per anuum, interest compounded annually.
The total interest paid to Rammu is

Answer

To find the total interest paid to Ramu after he invested Rs. 12,000 at a compound interest rate of 10% per annum for 3 years, we can follow these steps:

### Step 1: Identify the values
- Principal (P) = Rs. 12,000
- Rate of interest (R) = 10% per annum
- Time (T) = 3 years

### Step 2: Use the compound interest formula
The formula for calculating the amount (A) with compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]

### Step 3: Substitute the values into the formula
Substituting the values we have:
\[ A = 12000 \left(1 + \frac{10}{100}\right)^3 \]

### Step 4: Simplify the expression
First, calculate \( \frac{10}{100} \):
\[ \frac{10}{100} = 0.1 \]
So, the expression becomes:
\[ A = 12000 \left(1 + 0.1\right)^3 \]
\[ A = 12000 \left(1.1\right)^3 \]

### Step 5: Calculate \( (1.1)^3 \)
Now, calculate \( (1.1)^3 \):
\[ (1.1)^3 = 1.1 \times 1.1 \times 1.1 = 1.331 \]

### Step 6: Calculate the total amount
Now substitute back into the equation:
\[ A = 12000 \times 1.331 \]
\[ A = 15972 \]

### Step 7: Calculate the compound interest
The compound interest (CI) is calculated as:
\[ CI = A - P \]
Substituting the values:
\[ CI = 15972 - 12000 \]
\[ CI = 3972 \]

### Conclusion
The total interest paid to Ramu is Rs. 3,972.

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