The sum of money which when given on compound interest at 18% per annum would fetch ₹960 more when the interest is payable half yearly than when it was payable annually for 2 years is:

Let principal amount = Rs. $$x$$ and rate of interest = 18%

Compound interest when compounded annually = $$P(1+\frac{R}{100})^T$$

= $$x(1+\frac{18}{100})^2=(\frac{118}{100})^2x$$

= Rs. $$1.3924x$$

Compound interest when compounded half yearly = $$P(1+\frac{R}{200})^{2T}$$

= $$x(1+\frac{18}{200})^4=(\frac{109}{100})^4x$$

= Rs. $$1.41158161x$$

According to ques, => $$(1.41158161x-1.3924x)=960$$

=> $$0.01918161x=960$$

=> $$x=\frac{960}{0.01918161}\approx50047.93$$

$$\therefore$$ Sum of money given = Rs. 50,000

=> Ans - (B)