If Rs. 1000 becomes Rs. 1102.50 in 2 years. What is the compound interest rate?

Options

A. `5%` annual
B. `4%` annual
C. `7%` annual
D. `6%` annual

Answer

To find the compound interest rate when Rs. 1000 becomes Rs. 1102.50 in 2 years, we can use the formula for compound interest:

**Step 1: Identify the variables in the compound interest formula.**
The formula for compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where:
- \( A \) = Amount after time \( T \) (Rs. 1102.50)
- \( P \) = Principal amount (Rs. 1000)
- \( R \) = Rate of interest (unknown)
- \( T \) = Time in years (2 years)

**Step 2: Substitute the known values into the formula.**
Substituting the known values into the formula, we have:
\[ 1102.50 = 1000 \left(1 + \frac{R}{100}\right)^2 \]

**Step 3: Simplify the equation.**
Divide both sides by 1000:
\[ \frac{1102.50}{1000} = \left(1 + \frac{R}{100}\right)^2 \]
This simplifies to:
\[ 1.1025 = \left(1 + \frac{R}{100}\right)^2 \]

**Step 4: Take the square root of both sides.**
Taking the square root of both sides gives:
\[ \sqrt{1.1025} = 1 + \frac{R}{100} \]
Calculating the square root:
\[ 1.05 = 1 + \frac{R}{100} \]

**Step 5: Isolate \( R \).**
Subtract 1 from both sides:
\[ 1.05 - 1 = \frac{R}{100} \]
This simplifies to:
\[ 0.05 = \frac{R}{100} \]

**Step 6: Solve for \( R \).**
Multiply both sides by 100 to find \( R \):
\[ R = 0.05 \times 100 = 5 \]

Thus, the compound interest rate is **5%**.