The difference between simple interest and compound on Rs. 1400 for one year at 10% per annum reckoned half-yearly is: 

Given:

Principal (P) = Rs. 1400

Rate of Interest (R) = 10% per annum

Time (T) = 1 year

Interest compounded half-yearly

Concept:

Simple Interest (SI) is calculated using the formula:

SI = P × R × T / 100

Compound Interest (CI) when compounded half-yearly is calculated using the formula:

CI = P × (1 + (R / 2) / 100)^2T - P

Calculation:

Step 1: Calculate Simple Interest (SI)

⇒ SI = 1400 × 10 × 1 / 100

⇒ SI = Rs. 140

Step 2: Calculate Compound Interest (CI)

⇒ CI = 1400 × (1 + (10 / 2) / 100)² - 1400

⇒ CI = 1400 × (1 + 5 / 100)² - 1400

⇒ CI = 1400 × (1.05)² - 1400

⇒ CI = 1400 × 1.1025 - 1400

⇒ CI = 1543.5 - 1400

⇒ CI = Rs. 143.5

Step 3: Find the difference between CI and SI

⇒ Difference = CI - SI

⇒ Difference = 143.5 - 140

⇒ Difference = Rs. 3.5

∴ The difference between simple interest and compound interest is Rs. 3.5, hence the correct answer is option 2.

Shortcut Trick

Rate = 10/2 = 5%

Time = 2 (6 month + 6 month according to half yearly)

Difference of SI and CI for 2 years = P(R/100)²

⇒ 1400 × 25/10000

⇒ Rs. 3.5

∴ The difference between simple interest and compound interest is Rs. 3.5