Question
There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate?
Answer: Option C
$$\eqalign{
& {\text{Let}}\,{\text{P = Rs}}{\text{.}}\,{\text{100}}\,{\text{Then}},\, \cr
& \,\,\,\,\,{\text{S}}{\text{.I}}{\text{. = }}\,{\text{Rs}}{\text{.}}\,{\text{60}}\,{\text{and}} \cr
& \,\,\,\,\,\,\,\,{\text{T = 6}}\,{\text{years}} \cr
& \therefore R = {\frac{{100 \times 60}}{{100 \times 6}}} = 10\% \,p.a. \cr
& {\text{Now}},\,P = Rs.\,12000 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,T = 3\,{\text{year}}\,{\text{and}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,R = \,10\% \,p.a. \cr
& \therefore {\text{C}}{\text{.I}}{\text{.}} = Rs.\,\left[ {12000 \times \left\{ {{{\left( {1 + \frac{{10}}{{100}}} \right)}^3} - 1} \right\}} \right] \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {12000 \times \frac{{331}}{{1000}}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,3972 \cr} $$
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$$\eqalign{
& {\text{Let}}\,{\text{P = Rs}}{\text{.}}\,{\text{100}}\,{\text{Then}},\, \cr
& \,\,\,\,\,{\text{S}}{\text{.I}}{\text{. = }}\,{\text{Rs}}{\text{.}}\,{\text{60}}\,{\text{and}} \cr
& \,\,\,\,\,\,\,\,{\text{T = 6}}\,{\text{years}} \cr
& \therefore R = {\frac{{100 \times 60}}{{100 \times 6}}} = 10\% \,p.a. \cr
& {\text{Now}},\,P = Rs.\,12000 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,T = 3\,{\text{year}}\,{\text{and}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,R = \,10\% \,p.a. \cr
& \therefore {\text{C}}{\text{.I}}{\text{.}} = Rs.\,\left[ {12000 \times \left\{ {{{\left( {1 + \frac{{10}}{{100}}} \right)}^3} - 1} \right\}} \right] \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {12000 \times \frac{{331}}{{1000}}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,3972 \cr} $$
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