If the compound interest on a certain sum for two years at 12% per annum is Rs. 2544, the simple interest on it at the same rate for 2 years will be

Answer

To solve the problem, we need to find the simple interest on a certain sum given that the compound interest for two years at 12% per annum is Rs. 2544.

### Step 1: Understand the relationship between Compound Interest (CI) and Principal (P)
The formula for Compound Interest (CI) is:
\[ CI = A - P \]
Where \( A \) is the total amount after the interest is applied, and \( P \) is the principal amount.

### Step 2: Calculate the amount (A) using the Compound Interest formula
The formula for the total amount after 2 years with compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^t \]
Where:
- \( r \) is the rate of interest (12%),
- \( t \) is the time in years (2 years).

Thus, we can express the compound interest as:
\[ CI = P \left(1 + \frac{12}{100}\right)^2 - P \]

### Step 3: Substitute the values into the equation
Given \( CI = 2544 \):
\[ 2544 = P \left(1 + \frac{12}{100}\right)^2 - P \]
\[ 2544 = P \left(1.12^2 - 1\right) \]

### Step 4: Calculate \( 1.12^2 \)
Calculating \( 1.12^2 \):
\[ 1.12^2 = 1.2544 \]
So,
\[ 2544 = P (1.2544 - 1) \]
\[ 2544 = P (0.2544) \]

### Step 5: Solve for Principal (P)
Now, we can solve for \( P \):
\[ P = \frac{2544}{0.2544} \]
Calculating this gives:
\[ P = 10000 \]

### Step 6: Calculate Simple Interest (SI)
Now that we have the principal, we can calculate the simple interest for 2 years at 12%:
The formula for Simple Interest (SI) is:
\[ SI = \frac{P \cdot r \cdot t}{100} \]
Substituting the values:
\[ SI = \frac{10000 \cdot 12 \cdot 2}{100} \]
\[ SI = \frac{240000}{100} \]
\[ SI = 2400 \]

### Final Answer
The simple interest on the sum at the same rate for 2 years is Rs. 2400.

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