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### Question

What is the difference between the simple interest and compound interest at the rate of 4% for 1 year? The compounding is half-yearly, and the principal is Rs. 50000.

**A**

Rs. 20.

**B**

Rs. 120.

**C**

Rs. 70.

**D**

Rs. 220.

**Soln.**

**Ans: a**

The simple interest SI = (P × r)/100 = (50000 × 4)/100 = Rs. 2000. Compound interest will have half interest rate and n = 2. By shortcut formula, we have CI = ${P × R × (R + 200)}/10000$ = ${50000 × 2 × (2 + 200)}/10000$ = Rs. 2020. The difference = Rs. 20.