At what rate percent per annum will Rs. 2304 amounts to Rs. 2500 in 2 years at compound Interest?

Options

A. `4(1)/2%`
B. `4(1)/5%`
C. `4(1)/6%`
D. `4(1)/3%`

Answer

To solve the problem of finding the rate percent per annum at which Rs. 2304 amounts to Rs. 2500 in 2 years at compound interest, we can follow these steps:

### Step 1: Understand 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:
- \( A \) = Amount after time \( N \)
- \( P \) = Principal amount (initial investment)
- \( R \) = Rate of interest per annum
- \( N \) = Number of years

### Step 2: Substitute the known values
In this case:
- \( A = 2500 \)
- \( P = 2304 \)
- \( N = 2 \)

Substituting these values into the formula gives:
\[ 2500 = 2304 \left(1 + \frac{R}{100}\right)^2 \]

### Step 3: Isolate the term with \( R \)
To isolate \( \left(1 + \frac{R}{100}\right)^2 \), divide both sides by 2304:
\[ \left(1 + \frac{R}{100}\right)^2 = \frac{2500}{2304} \]

### Step 4: Simplify the fraction
Calculating the fraction:
\[ \frac{2500}{2304} = 1.0868 \quad (\text{approximately}) \]

### Step 5: Take the square root
Now, take the square root of both sides:
\[ 1 + \frac{R}{100} = \sqrt{1.0868} \]
Calculating the square root gives:
\[ 1 + \frac{R}{100} \approx 1.043 \]

### Step 6: Solve for \( R \)
Subtract 1 from both sides:
\[ \frac{R}{100} \approx 0.043 \]
Now, multiply by 100 to find \( R \):
\[ R \approx 4.3 \]

### Conclusion
Thus, the rate percent per annum is approximately:
\[ \boxed{4.3\%} \]