Saleem borrowed Rs. 20000 at compound interest and paid Rs. 22050 after 2 years to clear the debt. Find the rate of interest.

Options

A. 0.03
B. 0.05
C. 0.04
D. 0.07

Explanation

To find the rate of interest that Saleem paid on his loan, we can use the formula for compound interest. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Principal (P) = Rs. 20,000
- Amount after 2 years (A) = Rs. 22,050
- Time (N) = 2 years

### Step 2: Use the formula for compound interest
The formula for the amount A in compound interest is given by:
\[ A = P \left(1 + \frac{R}{100}\right)^N \]

### Step 3: Substitute the known values into the formula
Substituting the values we have:
\[ 22,050 = 20,000 \left(1 + \frac{R}{100}\right)^2 \]

### Step 4: Divide both sides by the principal
To isolate the compound interest term, divide both sides by 20,000:
\[ \frac{22,050}{20,000} = \left(1 + \frac{R}{100}\right)^2 \]
\[ 1.1025 = \left(1 + \frac{R}{100}\right)^2 \]

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

### Step 6: Solve for R
Now, subtract 1 from both sides:
\[ 1.05 - 1 = \frac{R}{100} \]
\[ 0.05 = \frac{R}{100} \]

### Step 7: Multiply by 100 to find R
Multiply both sides by 100 to find the rate of interest:
\[ R = 0.05 \times 100 \]
\[ R = 5 \]

### Conclusion
The rate of interest is **5%**.

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