At what rate per cent per annum will a sum of Rs.1000 amount to Rs.1,102.50 in…

Step-by-Step Solution

To find the annual rate of interest, we can use the standard compound interest formula.

1. Understand the given variables:

   • Principal (P) = Rs. 1,000

   • Amount (A) = Rs. 1,102.50

   • Time (n) = 2 years

   • Rate (R) = ?

2. Use the compound interest formula: A = P * (1 + R/100)^n 1,102.50 = 1,000 * (1 + R/100)^2

3. Solve for R:

   • Divide both sides by 1,000: 1,102.50 / 1,000 = (1 + R/100)^2 1.1025 = (1 + R/100)^2

   • Take the square root of both sides: sqrt(1.1025) = 1 + R/100 1.05 = 1 + R/100

   • Subtract 1 from both sides: 0.05 = R/100

   • Multiply by 100: R = 5%