The difference between the simple interest and compound interest(compounded half-yearly) on a certain sum at 10% per annum for one year is ₹ 100. The principal sum is equal to

Correct option is D

Given:
Difference = ₹100
Time = 1 year
Rate = 10% per annum, compounded half-yearly
Formula Used:
When compounded half-yearly, Rate R' =$$\frac{R}{2}$$​, Time T' = 2T.
Difference for 2 periods = $$P(\frac{R'}{100})^2$$​​
Solution:
Effective rate per half-year = $$\frac{10}{2} = 5\%$$​​
Number of half-years = 1 × 2 = 2
The SI for 1 year is equivalent to SI for 2 half-years at 5%.
The difference between CI and SI for 2 periods is given by $$P(\frac{5}{100})^2.$$​​
​$$100 = P(\frac{1}{20})^2$$​​
100 = $$P × \frac{1}{400}$$​​
P = 100 × 400 = 40000
Final Answer
So the correct answer is (d)