The effective annual rate of interest corresponding to a nominal rate of 22% per annum payable half-yearly is

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

Rate of interest = 22% under compound interest half yearly

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

= $$100x (1 + \frac{22}{200})^{2 \times 1}$$

= $$100x (\frac{111}{100})^2 = \frac{111 \times 111 \times x}{100}$$

= Rs. $$123.21 x$$

=> Compound Interest = Rs. $$(123.21 x - 100x)$$ = Rs. $$23.21 x$$

$$\therefore$$ Effective rate of interest = $$\frac{23.21 x}{100x} \times 100$$

= $$23.21 \%$$