The differecnce between the compound interest and th simple interest on a certain sum for 3 years at 10% per annum is Rs 93. Find the sum.

Answer

To find the sum (principal) based on the difference between compound interest (CI) and simple interest (SI) over 3 years at a rate of 10% per annum, we can follow these steps:

### Step 1: Understand the formulas
- The formula for **Simple Interest (SI)** is:
\[ SI = \frac{P \times R \times T}{100} \]
where \( P \) is the principal, \( R \) is the rate of interest, and \( T \) is the time in years.

- The formula for **Compound Interest (CI)** is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
where \( A \) is the amount after time \( T \), and the compound interest can be calculated as:
\[ CI = A - P \]

### Step 2: Calculate Simple Interest for 3 years
Given:
- \( R = 10\% \)
- \( T = 3 \)

Using the SI formula:
\[ SI = \frac{P \times 10 \times 3}{100} = \frac{30P}{100} = 0.3P \]

### Step 3: Calculate Compound Interest for 3 years
Using the CI formula:
\[ A = P \left(1 + \frac{10}{100}\right)^3 = P \left(1.1\right)^3 \]
Calculating \( (1.1)^3 \):
\[ (1.1)^3 = 1.331 \]
Thus,
\[ A = 1.331P \]
Now, the compound interest is:
\[ CI = A - P = 1.331P - P = 0.331P \]

### Step 4: Find the difference between CI and SI
The difference between the compound interest and simple interest is given as Rs 93:
\[ CI - SI = 93 \]
Substituting the values we found:
\[ 0.331P - 0.3P = 93 \]
This simplifies to:
\[ 0.031P = 93 \]

### Step 5: Solve for the principal \( P \)
To find \( P \):
\[ P = \frac{93}{0.031} = 3000 \]

### Final Answer
The sum (principal) is Rs 3000.

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