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

Step 1: For 1 year compounded half yearly at annual rate \( R\% \), the half yearly rate is \( r=\frac{R}{200} \). The compound amount factor is \( (1+r)^2 \), and the simple interest factor for the same year is \( 1+2r \).

Step 2: The difference between compound interest and simple interest, as a fraction of the principal, is \( (1+r)^2-(1+2r)=r^2 \).

Step 3: Here \( r=\frac{10}{200}=0.05 \), so \( r^2=0.0025 \). The difference in rupees is \( 500 \times 0.0025=1.25 \).
\[ \boxed{\text{Rs. } 1.25} \]

Answer 2

Track the principal through each half-year under compounding: starting at Rs. 500, after the first half-year it grows by 5 percent to \( 500+25=525 \), and after the second half-year it grows by another 5 percent, on the larger base, to \( 525+26.25=551.25 \). This gives a compound interest of \( 551.25-500=51.25 \) for the year. We can check each option against the difference between this figure and the flat simple interest of \( 500 \times 10\%=50 \).

1. Rs. 1: The tracked difference is \( 51.25-50=1.25 \), not Rs. 1.
2. Rs. 1.25: The tracked difference is \( 51.25-50=1.25 \), matching exactly.
3. Rs. 1.5: The tracked difference is Rs. 1.25, not Rs. 1.5.
4. Rs. 2: The tracked difference is Rs. 1.25, well short of Rs. 2.

Tracking the principal through both half-years gives a compound amount of Rs. 551.25 against a flat simple interest amount of Rs. 550, a difference of exactly Rs. 1.25.

Therefore, the correct answer is Rs. 1.25.