The effective annual rate of interest corresponding to a nominal rate of 15% per annum payable half-yearly is

Let sum be = Rs. $$100x$$

Rate of interest = 15% under compound interest half yearly

Amount after 1 year = $$P (1 + \frac{R}{2 \times 100})^{2 \times T}$$

= $$100x (1 + \frac{15}{200})^{2 \times 1}$$

= $$100x (\frac{43}{40})^2 = \frac{43 \times 43 \times x}{16}$$

= Rs. $$115.5625 x$$

=> Compound Interest = Rs. $$(115.5625 x - 100x)$$ = Rs. $$15.5625 x$$

$$\therefore$$ Effective rate of interest = $$\frac{15.5625 x}{100x} \times 100$$

$$\approx 15.56 \%$$

=> Ans - (A)