At what percent per annum will Rs. 3000/- amount to Rs. 3993/- in 3 years if the interest is compounded annually?

Options

A. 9%
B. 10%
C. 11%
D. 13%

Answer

To solve the problem of finding the rate of interest per annum at which Rs. 3000 amounts to Rs. 3993 in 3 years with compounded interest, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Principal (P) = Rs. 3000
- Amount (A) = Rs. 3993
- Time (t) = 3 years

2. **Use the Compound Interest Formula:**
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^t \]
Where:
- \( A \) = Amount after time \( t \)
- \( P \) = Principal amount
- \( r \) = Rate of interest per annum
- \( t \) = Time in years

3. **Substitute the Known Values into the Formula:**
\[ 3993 = 3000 \left(1 + \frac{r}{100}\right)^3 \]

4. **Divide Both Sides by 3000:**
\[ \frac{3993}{3000} = \left(1 + \frac{r}{100}\right)^3 \]
Simplifying the left side:
\[ 1.331 = \left(1 + \frac{r}{100}\right)^3 \]

5. **Take the Cube Root of Both Sides:**
To eliminate the exponent, take the cube root:
\[ 1 + \frac{r}{100} = \sqrt[3]{1.331} \]
The cube root of \( 1.331 \) is \( 1.1 \):
\[ 1 + \frac{r}{100} = 1.1 \]

6. **Solve for \( r \):**
Subtract 1 from both sides:
\[ \frac{r}{100} = 1.1 - 1 \]
\[ \frac{r}{100} = 0.1 \]
Multiply both sides by 100:
\[ r = 10 \]

7. **Conclusion:**
The rate of interest per annum is \( \boxed{10\%} \).