At what rate per cent per annum will Rs 4000 amount to Rs 4410 in 2 years when compounded annually?s

Answer

To solve the problem of finding the rate of interest per annum at which Rs 4000 will amount to Rs 4410 in 2 years when compounded annually, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Principal (P) = Rs 4000
- Amount (A) = Rs 4410
- Time (T) = 2 years

2. **Use the formula for compound interest:**
The formula for the amount (A) in compound interest is given by:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
where:
- \( A \) = final amount
- \( P \) = principal amount
- \( r \) = rate of interest per annum
- \( n \) = number of years

3. **Substitute the known values into the formula:**
\[ 4410 = 4000 \left(1 + \frac{r}{100}\right)^2 \]

4. **Divide both sides by 4000 to isolate the term with \( r \):**
\[ \frac{4410}{4000} = \left(1 + \frac{r}{100}\right)^2 \]
\[ 1.1025 = \left(1 + \frac{r}{100}\right)^2 \]

5. **Take the square root of both sides:**
\[ \sqrt{1.1025} = 1 + \frac{r}{100} \]
\[ 1.05 = 1 + \frac{r}{100} \]

6. **Subtract 1 from both sides:**
\[ 1.05 - 1 = \frac{r}{100} \]
\[ 0.05 = \frac{r}{100} \]

7. **Multiply both sides by 100 to find \( r \):**
\[ r = 0.05 \times 100 \]
\[ r = 5 \]

8. **Conclusion:**
The rate of interest per annum is **5%**.