The simple interest on a sum of money for 2 years at 8% per annum is Rs 2400. What will be the compound interest on that sume rate and for the same period?

Answer

To solve the problem step by step, we will first determine the principal amount using the given simple interest, and then we will calculate the compound interest.

### Step 1: Find the Principal Amount (P)
The formula for Simple Interest (SI) is given by:

\[ SI = \frac{P \times R \times T}{100} \]

Where:
- \( SI \) = Simple Interest (Rs 2400)
- \( R \) = Rate of interest (8%)
- \( T \) = Time period (2 years)

Substituting the known values into the formula:

\[ 2400 = \frac{P \times 8 \times 2}{100} \]

### Step 2: Simplify the Equation
Now, we can simplify the equation to find \( P \):

\[ 2400 = \frac{16P}{100} \]

Multiplying both sides by 100 to eliminate the fraction:

\[ 240000 = 16P \]

### Step 3: Solve for P
Now, divide both sides by 16:

\[ P = \frac{240000}{16} = 15000 \]

So, the principal amount \( P \) is Rs 15000.

### Step 4: Calculate the Amount (A) using Compound Interest Formula
The formula for Compound Interest (CI) is:

\[ A = P \left(1 + \frac{R}{100}\right)^T \]

Where:
- \( A \) = Amount after time \( T \)
- \( R \) = Rate of interest (8%)
- \( T \) = Time period (2 years)

Substituting the values:

\[ A = 15000 \left(1 + \frac{8}{100}\right)^2 \]

### Step 5: Simplify the Calculation
Calculating \( 1 + \frac{8}{100} \):

\[ A = 15000 \left(1 + 0.08\right)^2 = 15000 \left(1.08\right)^2 \]

Calculating \( (1.08)^2 \):

\[ (1.08)^2 = 1.1664 \]

Now substitute back into the equation for \( A \):

\[ A = 15000 \times 1.1664 = 17496 \]

### Step 6: Calculate Compound Interest (CI)
Now, we can find the Compound Interest using the formula:

\[ CI = A - P \]

Substituting the values we found:

\[ CI = 17496 - 15000 = 2496 \]

### Final Answer
The compound interest on the sum for the same rate and period is Rs 2496.

---