The effective annual rate of interest corresponding to a nominal rate of 7% per annum payable half­yearly is

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

Rate of interest = 7% under compound interest half yearly

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

= $$100x (1 + \frac{7}{200})^{2 \times 1}$$

= $$100x (\frac{207}{200})^2 = \frac{207 \times 207 \times x}{400}$$

= Rs. $$107.12 x$$

=> Compound Interest = Rs. $$(107.12 x - 100x)$$ = Rs. $$7.12 x$$

$$\therefore$$ Effective rate of interest = $$\frac{7.12 x}{100x} \times 100$$

= $$7.12 \%$$