A person borrows Rs. 7,000 for 3 year's at 5% p.a. simple interest. He immediately lends it to another person at $$6\frac{1}{3}\% $$  p.a. for 3 years. Find the gain in the transaction per year.

Solution (By Examveda Team)

$$\eqalign{ & {\bf{Given:}} \cr & {P_1} = 7000,\,{T_1} = 3{\text{ years, }}{R_1} = 5\% \cr & {P_1} = 7000,\,{T_2} = 3{\text{ years, }}{R_2} = 6\frac{1}{3}\% \cr & {\bf{Formula}}\,{\bf{used:}} \cr & {\text{S}}{\text{.I}}{\text{.}} = \frac{{{\text{Principal amout}} \times {\text{Rate of interest}} \times {\text{Time}}}}{{100}} \cr & {\bf{Calculation:}} \cr & {\text{S}}{\text{.I}}{{\text{.}}_1} = \frac{{{P_1} \times {R_1} \times {T_1}}}{{100}} \cr & = \frac{{7000 \times 5 \times 3}}{{100}} \cr & = 1050 \cr & {\text{S}}{\text{.I}}{{\text{.}}_1}{\text{ for one year}} = \frac{{1050}}{3} = 350 \cr & {\text{S}}{\text{.I}}{{\text{.}}_2} = \frac{{{P_1} \times {R_2} \times {T_2}}}{{100}} \cr & = \frac{{7000 \times \frac{{19}}{3} \times 3}}{{100}} \cr & = 1330 \cr & {\text{S}}{\text{.I}}{{\text{.}}_2}{\text{ for one year}} = \frac{{1330}}{3} = 443.33 \cr & {\text{Gain for one year}} = 443.33 - 350 = 93.33 \cr & \therefore {\text{He gain in the transaction per year 93}}{\text{.33}} \cr} $$