The difference between simple interest and compound on Rs. 1200 for one year…

Step-by-Step Solution

To find the difference between simple interest and compound interest for one year at 10% per annum, compounded half-yearly, we calculate each separately.

1. Calculate Simple Interest (SI):

   • Principal (P) = 1200

   • Rate (R) = 10% per annum

   • Time (T) = 1 year

   • SI = (P * R * T) / 100

   • SI = (1200 * 10 * 1) / 100 = Rs. 120

2. Calculate Compound Interest (CI) compounded half-yearly:

   • When interest is compounded half-yearly, the rate is halved and the number of periods is doubled.

   • Rate per half-year = 10% / 2 = 5%

   • Number of half-years in 1 year = 2

   • Amount (A) = P * (1 + R/100)^n

   • A = 1200 * (1 + 5/100)^2

   • A = 1200 * (1.05)^2

   • A = 1200 * 1.1025 = Rs. 1323

   • CI = A - P = 1323 - 1200 = Rs. 123

3. Find the Difference:

   • Difference = CI - SI

   • Difference = 123 - 120 = Rs. 3