On what sum of money will the difference between the compound interest and simple interest for 3 years be equal to Rs 930, if the rate of interest charged for both is 10% p.a ?

Answer

To solve the problem of finding the sum of money (P) for which the difference between compound interest (CI) and simple interest (SI) over 3 years at a rate of 10% per annum is Rs 930, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formulas**:
- The formula for **Simple Interest (SI)** is:
\[ SI = \frac{P \times r \times t}{100} \]
- The formula for **Compound Interest (CI)** is:
\[ CI = P \left(1 + \frac{r}{100}\right)^t - P \]

2. **Substitute the known values**:
- Here, the rate \( r = 10\% \) and time \( t = 3 \) years.
- For **SI**:
\[ SI = \frac{P \times 10 \times 3}{100} = \frac{30P}{100} = 0.3P \]
- For **CI**:
\[ CI = P \left(1 + \frac{10}{100}\right)^3 - P = P \left(1.1^3\right) - P \]

3. **Calculate \( 1.1^3 \)**:
- Calculate \( 1.1^3 \):
\[ 1.1^3 = 1.1 \times 1.1 \times 1.1 = 1.331 \]
- Therefore,
\[ CI = P(1.331) - P = 0.331P \]

4. **Set up the equation for the difference**:
- The difference between CI and SI is given as Rs 930:
\[ CI - SI = 930 \]
- Substitute the values of CI and SI:
\[ 0.331P - 0.3P = 930 \]

5. **Simplify the equation**:
- Combine like terms:
\[ 0.031P = 930 \]

6. **Solve for \( P \)**:
- Divide both sides by 0.031:
\[ P = \frac{930}{0.031} \]
- Calculate \( P \):
\[ P = 30000 \]

### Final Answer:
The sum of money (P) is Rs 30,000.