Find the sum on which the compound interest for 3 years at 10% per annum amounts to Rs 1,655

Answer

To find the sum (principal amount) on which the compound interest for 3 years at 10% per annum amounts to Rs 1,655, we can use the formula for compound interest.

### Step-by-step Solution:

1. **Understand the Given Information:**
- Compound Interest (CI) = Rs 1,655
- Rate of Interest (R) = 10% per annum
- Time (T) = 3 years

2. **Use the Compound Interest Formula:**
The formula for compound interest is:
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]
Where:
- \( CI \) = Compound Interest
- \( P \) = Principal amount
- \( R \) = Rate of interest
- \( T \) = Time in years

3. **Rearranging the Formula:**
We can rearrange the formula to find the principal amount \( P \):
\[ CI + P = P \left(1 + \frac{R}{100}\right)^T \]
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]
\[ CI = P \left[\left(1 + \frac{R}{100}\right)^T - 1\right] \]
\[ P = \frac{CI}{\left(1 + \frac{R}{100}\right)^T - 1} \]

4. **Substituting the Values:**
Substitute \( CI = 1655 \), \( R = 10 \), and \( T = 3 \):
\[ P = \frac{1655}{\left(1 + \frac{10}{100}\right)^3 - 1} \]
\[ P = \frac{1655}{\left(1 + 0.1\right)^3 - 1} \]
\[ P = \frac{1655}{(1.1)^3 - 1} \]

5. **Calculating \( (1.1)^3 \):**
\[ (1.1)^3 = 1.1 \times 1.1 \times 1.1 = 1.331 \]
So,
\[ P = \frac{1655}{1.331 - 1} \]
\[ P = \frac{1655}{0.331} \]

6. **Final Calculation:**
\[ P = 1655 \div 0.331 \approx 5000 \]

Thus, the principal amount \( P \) is Rs 5,000.