At what rate per cent per annum will Rs 5000 amount to Rs 5832 in 2 years, compounded annually?

Options

A. 0.11
B. 0.1
C. 0.09
D. 0.08

Answer

To solve the problem of finding the rate of interest per annum at which Rs 5000 will amount to Rs 5832 in 2 years, compounded annually, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Principal (P) = Rs 5000
- Amount (A) = Rs 5832
- Time (n) = 2 years

2. **Use the Compound Interest Formula:**
The formula for the amount in compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
where \( r \) is the rate of interest.

3. **Substitute the Known Values into the Formula:**
\[ 5832 = 5000 \left(1 + \frac{r}{100}\right)^2 \]

4. **Divide Both Sides by 5000:**
\[ \frac{5832}{5000} = \left(1 + \frac{r}{100}\right)^2 \]

5. **Calculate the Left Side:**
\[ \frac{5832}{5000} = 1.1664 \]
So, we have:
\[ 1.1664 = \left(1 + \frac{r}{100}\right)^2 \]

6. **Take the Square Root of Both Sides:**
\[ \sqrt{1.1664} = 1 + \frac{r}{100} \]
Calculating the square root:
\[ 1.08 = 1 + \frac{r}{100} \]

7. **Isolate \( r \):**
\[ \frac{r}{100} = 1.08 - 1 \]
\[ \frac{r}{100} = 0.08 \]

8. **Multiply by 100 to Find \( r \):**
\[ r = 0.08 \times 100 = 8 \]

9. **Conclusion:**
Therefore, the rate of interest is:
\[ \text{Rate} = 8\% \text{ per annum} \]