A certain sum of amounts to Rs. 5832 in 2 years at 8% per annum compound…

Step-by-Step Solution

To find the principal sum, we use the compound interest formula, which relates the principal (P), the interest rate (R), the time (T), and the final amount (A).

1. Understand the relationship:

   • Formula: A = P * (1 + R/100)^T

   • Given: A = Rs. 5832, R = 8%, T = 2 years.

2. Convert the rate to a fraction:

   • R = 8% = 8/100 = 2/25.

   • This means for every 25 units of principal, the amount becomes 27 units after one year (25 + 2).

3. Apply the ratio method over 2 years:

   • Year 1: Principal 25 -> Amount 27

   • Year 2: Principal 25 -> Amount 27

   • Over 2 years, the ratio of Principal to Amount is (25 * 25) : (27 * 27) = 625 : 729.

4. Solve for the Principal:

   • We know that 729 units correspond to Rs. 5832.

   • To find the value of 1 unit: 5832 / 729 = 8.

   • The principal is 625 units: 625 * 8 = Rs. 5000.