At what rate per cent per annum will Rs. 1000 amount to Rs. 1331 in 3 years. The interest is compounded yearly

Answer

To solve the problem of finding the rate of interest per annum that will allow Rs. 1000 to amount to Rs. 1331 in 3 years with compounded interest, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Principal (P) = Rs. 1000
- Amount (A) = Rs. 1331
- Time (t) = 3 years
- Rate of interest (r) = ?

2. **Use the Compound Interest Formula**:
The formula for compound interest is given by:
\[ A = P \left(1 + \frac{r}{100}\right)^t \]
Plugging in the known values:
\[ 1331 = 1000 \left(1 + \frac{r}{100}\right)^3 \]

3. **Rearranging the Equation**:
Divide both sides by 1000:
\[ \frac{1331}{1000} = \left(1 + \frac{r}{100}\right)^3 \]
This simplifies to:
\[ 1.331 = \left(1 + \frac{r}{100}\right)^3 \]

4. **Taking the Cube Root**:
To isolate \(1 + \frac{r}{100}\), take the cube root of both sides:
\[ 1 + \frac{r}{100} = \sqrt[3]{1.331} \]
We know that \(1.331\) is equal to \(\left(\frac{11}{10}\right)^3\), so:
\[ 1 + \frac{r}{100} = \frac{11}{10} \]

5. **Solving for \(r\)**:
Subtract 1 from both sides:
\[ \frac{r}{100} = \frac{11}{10} - 1 \]
This simplifies to:
\[ \frac{r}{100} = \frac{11}{10} - \frac{10}{10} = \frac{1}{10} \]

6. **Finding the Rate \(r\)**:
Multiply both sides by 100:
\[ r = 100 \times \frac{1}{10} = 10 \]

7. **Conclusion**:
Therefore, the rate of interest per annum is:
\[ r = 10\% \]