The simple interest on a sum of money for 3 years at 12% per annum is Rs 6750. What will be the compound interest on the same sum at the rate for the same period, compounded annually?

Answer

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

### Step 1: Find the Principal Amount

Given:
- Simple Interest (SI) = Rs 6750
- Rate of Interest (R) = 12% per annum
- Time (T) = 3 years

The formula for Simple Interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]

We can rearrange this formula to find the principal (P):
\[ P = \frac{\text{SI} \times 100}{R \times T} \]

Substituting the values:
\[ P = \frac{6750 \times 100}{12 \times 3} \]

Calculating the denominator:
\[ 12 \times 3 = 36 \]

Now substituting back:
\[ P = \frac{675000}{36} \]

Calculating the principal:
\[ P = 18750 \]

### Step 2: Calculate the Compound Interest

Now that we have the principal amount, we can calculate the compound interest using the formula:
\[ \text{Amount} (A) = P \left(1 + \frac{R}{100}\right)^T \]

Substituting the values:
\[ A = 18750 \left(1 + \frac{12}{100}\right)^3 \]

Calculating \(1 + \frac{12}{100}\):
\[ 1 + 0.12 = 1.12 \]

Now substituting this back into the formula:
\[ A = 18750 \times (1.12)^3 \]

Calculating \( (1.12)^3 \):
\[ (1.12)^3 = 1.404928 \]

Now substituting this value:
\[ A = 18750 \times 1.404928 \]

Calculating the amount:
\[ A \approx 26342.40 \]

### Step 3: Calculate the Compound Interest

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

Substituting the values we found:
\[ \text{CI} = 26342.40 - 18750 \]

Calculating the compound interest:
\[ \text{CI} \approx 7592.40 \]

### Final Answer
The compound interest on the same sum at the rate for the same period, compounded annually, is approximately Rs 7592.40.

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