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

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