Rs. 8000 invested at compound interest, gives Rs. 1261 as interest after 3 years. The rate of interest per annum is:

Answer

To find the rate of interest per annum when Rs. 8000 is invested at compound interest and yields Rs. 1261 as interest after 3 years, we can follow these steps:

### Step 1: Determine the Total Amount
First, we need to calculate the total amount after 3 years. The total amount (A) is the sum of the principal (P) and the compound interest (CI).

\[ A = P + CI \]

Given:
- Principal (P) = Rs. 8000
- Compound Interest (CI) = Rs. 1261

Substituting the values:

\[ A = 8000 + 1261 = 9261 \]

### Step 2: Use the Compound Interest Formula
The formula for compound interest is given by:

\[ A = P \left(1 + \frac{R}{100}\right)^T \]

Where:
- A = Total amount after time T
- P = Principal amount
- R = Rate of interest per annum
- T = Time in years

Substituting the known values into the formula:

\[ 9261 = 8000 \left(1 + \frac{R}{100}\right)^3 \]

### Step 3: Isolate the Term with R
To isolate the term with R, we first divide both sides by 8000:

\[ \frac{9261}{8000} = \left(1 + \frac{R}{100}\right)^3 \]

Calculating the left side:

\[ 1.157625 = \left(1 + \frac{R}{100}\right)^3 \]

### Step 4: Take the Cube Root
Next, we take the cube root of both sides to solve for \(1 + \frac{R}{100}\):

\[ 1 + \frac{R}{100} = \sqrt[3]{1.157625} \]

Calculating the cube root:

\[ 1 + \frac{R}{100} \approx 1.05 \]

### Step 5: Solve for R
Now, we can solve for R:

\[ \frac{R}{100} = 1.05 - 1 \]
\[ \frac{R}{100} = 0.05 \]
\[ R = 0.05 \times 100 = 5 \]

### Conclusion
The rate of interest per annum is:

\[ \boxed{5\%} \]

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