If the compound interest on a certain sum of money for 3 years at 10% p.a be ₹ 993. what would be the simple interest?

Options

A. ₹800
B. ₹950
C. ₹900
D. ₹1000

Explanation

To find the simple interest based on the given compound interest, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between Compound Interest (CI) and Simple Interest (SI):**
- The formula for Compound Interest for 3 years at a rate of 10% can be represented as:
\[ CI = P \left(1 + \frac{r}{100}\right)^n - P \]
- Where \( P \) is the principal amount, \( r \) is the rate of interest per annum, and \( n \) is the number of years.

2. **Given Information:**
- Compound Interest (CI) for 3 years = ₹993
- Rate of interest (r) = 10%
- Time (n) = 3 years

3. **Using the Compound Interest formula:**
- Rearranging the formula to find \( P \):
\[ 993 = P \left(1 + \frac{10}{100}\right)^3 - P \]
- Simplifying the equation:
\[ 993 = P \left(1.1^3 - 1\right) \]

4. **Calculate \( 1.1^3 \):**
- \( 1.1^3 = 1.331 \)
- Therefore, \( 1.1^3 - 1 = 1.331 - 1 = 0.331 \)

5. **Substituting back to find \( P \):**
- Now, substituting back:
\[ 993 = P \times 0.331 \]
- Solving for \( P \):
\[ P = \frac{993}{0.331} \approx 3000 \]

6. **Calculate Simple Interest (SI):**
- Now that we have \( P \), we can calculate the Simple Interest using the formula:
\[ SI = \frac{P \times r \times n}{100} \]
- Substituting the values:
\[ SI = \frac{3000 \times 10 \times 3}{100} = \frac{90000}{100} = 900 \]

7. **Final Answer:**
- The Simple Interest for 3 years at 10% p.a. is ₹900.