Sonika invested an amount of ₹5800 for 2 years. At what rate of compound interest will she get an amount of ₹594.50 at the end of two years?

Options

A. 5 pcpa
B. 4 pcpa
C. 6 pcpa
D. 8 pcpa

Explanation

To find the rate of compound interest at which Sonika will receive an amount of ₹594.50 after investing ₹5800 for 2 years, we can follow these steps:

### Step 1: Identify the principal amount and the total amount after 2 years
- Principal (P) = ₹5800
- Interest earned (I) = ₹594.50
- Total Amount (A) = Principal + Interest = ₹5800 + ₹594.50 = ₹6394.50

### Step 2: Use the formula for compound interest
The formula for the amount in compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Where:
- \( A \) = Total amount after time \( n \)
- \( P \) = Principal amount
- \( r \) = Rate of interest per annum
- \( n \) = Time in years

### Step 3: Substitute the known values into the formula
Substituting the values we have:
\[ 6394.50 = 5800 \left(1 + \frac{r}{100}\right)^2 \]

### Step 4: Divide both sides by the principal amount
\[ \frac{6394.50}{5800} = \left(1 + \frac{r}{100}\right)^2 \]
Calculating the left side:
\[ \frac{6394.50}{5800} = 1.1025 \]

### Step 5: Take the square root of both sides
To eliminate the square, we take the square root:
\[ \sqrt{1.1025} = 1 + \frac{r}{100} \]
Calculating the square root:
\[ 1.05 = 1 + \frac{r}{100} \]

### Step 6: Solve for the rate of interest
Now, we can isolate \( r \):
\[ \frac{r}{100} = 1.05 - 1 \]
\[ \frac{r}{100} = 0.05 \]
Multiplying both sides by 100:
\[ r = 5 \]

### Conclusion
The rate of compound interest is **5% per annum**.

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