An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes:

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{sum}}\,{\text{be}}\,{\text{Rs}}{\text{.}}\,{\text{100}}{\text{.}}\,{\text{Then,}} \cr & {\text{S}}{\text{.I}}{\text{.}}\,{\text{for}}\,{\text{first}}\,{\text{6}}\,{\text{months}} \cr & = Rs.\,\left( {\frac{{100 \times 10 \times 1}}{{100 \times 2}}} \right) \cr & = Rs.\,5 \cr & {\text{S}}{\text{.I}}{\text{.}}\,{\text{for}}\,{\text{last}}\,{\text{6}}\,{\text{months}} \cr & = Rs.\,\left( {\frac{{105 \times 10 \times 1}}{{100 \times 2}}} \right) \cr & = Rs.\,5.25 \cr} $$
So, amount at the end of 1 year
= Rs. (100 + 5 + 5.25)
= Rs. 110.25
∴ Effective rate = (110.25 - 100) = 10.25%