Find the rate of interest in case of compound interest compounded annually if…

Step-by-Step Solution

To find the rate of interest (r), we use the compound interest formula where the total amount (A) is the sum of the principal (P) and the compound interest (CI).

1. Identify the variables:

   • Principal (P) = 5000

   • Compound Interest (CI) = 1384.5

   • Time (t) = 2 years

   • Total Amount (A) = P + CI = 5000 + 1384.5 = 6384.5

2. Set up the compound interest formula:

   • A = P * (1 + r)^t

   • 6384.5 = 5000 * (1 + r)^2

3. Solve for r:

   • Divide both sides by 5000: (1 + r)^2 = 6384.5 / 5000 (1 + r)^2 = 1.2769

   • Take the square root of both sides: 1 + r = square root of 1.2769 1 + r = 1.13

   • Subtract 1 from both sides: r = 0.13

4. Convert to percentage:

   • r = 0.13 * 100 = 13%