Question

The difference between Simple Interest and Compound Interest on Rs. 500 for 1 year at 10% per annum, reckoned half yearly is

• A. Rs. 1
• B. Rs. 1.25
• C. Rs. 1.5
• D. Rs. 2

Hint:

For compound interest, ensure that the rate is halved and the time is doubled for half-yearly compounding.

Answer 1

The Correct Option is B

The formula for Simple Interest (SI) is: \[ SI = \frac{P \times R \times T}{100} \] For Rs. 500 at 10% per annum for 1 year: \[ SI = \frac{500 \times 10 \times 1}{100} = 50 \] The formula for Compound Interest (CI) when interest is compounded half yearly is: \[ CI = P \left(1 + \frac{R}{2 \times 100}\right)^{2T} - P \] For Rs. 500 at 10% per annum for 1 year: \[ CI = 500 \left(1 + \frac{10}{2 \times 100}\right)^{2} - 500 = 500 \left(1 + 0.05\right)^2 - 500 \] \[ CI = 500 \times 1.1025 - 500 = 551.25 - 500 = 51.25 \] The difference between CI and SI is: \[ 51.25 - 50 = 1.25 \] Thus, the difference is Rs. 1.25.