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