Question

how many years the amount for rupees 10000 becomes rupees12100 10% compound interest​

Answer 1

$\bf \: \underline{Given} :$ ↴

$\sf \: Principal : Rs. \: 10000$

$\sf \: Amount : Rs. \: 12100$

$\sf \: Rate : 10 \: \%$

$\bf \: \underline{To \: find} :$ ↴

$\sf \: We \: have \: to \: find \: the \: (n \: years) \: Time.$

$\sf \: As \: we \: know \: that,$

$\boxed{ \pink{\sf {Amount = { P \Bigg( 1 + \dfrac{R}{100} \Bigg )}^{n} } } }$

$\sf \: \underline{Putting \: the \: values.}$

$\sf {12100 = {10000 \: \Bigg ( 1 + \dfrac{10}{100} \Bigg) }^{n} }$

$\sf {12100 = {10000 \: \Bigg ( \dfrac{100 + 10}{100} \Bigg )}^{n} }$

$\sf {12100 = {10000 \: \Bigg ( \dfrac{110}{100} \Bigg )}^{n} }$

$\sf {\dfrac{12100}{10000} = {\Bigg ( \dfrac{11}{10} \Bigg )}^{n} }$

$\sf {\dfrac{121}{100} = {\Bigg ( \dfrac{11}{10} \Bigg )}^{n} }$

$\sf { {\Bigg ( \dfrac{11}{10} \Bigg )}^{2} } \: = \: { {\Bigg ( \dfrac{11}{10} \Bigg )}^{n} }$

$\sf \: Here \: the \: Base \: is \: equal..$

$\sf \: So, \: the \: another \: power \: must \: be \: equal.$

$\rm \: Now, \: Our \: answer \: is :$

$\pink { \star} \: \green{ \boxed { \orange{ \large \sf {2 = n } }} \:\pink { \star} }$

Answer 2

$\ \sf{{«\: คꈤ \mathfrak Sฬєя \: » }} \: \: \: \: \: \: \underline {\underline{ \red{\sf {Amount }}}}={{{ \green { P \Bigg( 1 + \dfrac{R}{100} \Bigg )}^{n} } } } \\ \\ ⇛\sf {12100 = {10000 \: \Bigg ( 1 + \dfrac{10}{100} \Bigg) }^{n} } \\ \\ ⇛\sf {12100 = {10000 \: \Bigg ( \dfrac{100 + 10}{100} \Bigg )}^{n} } \\ \\⇛ \sf {12100 = {10000 \: \Bigg ( \dfrac{110}{100} \Bigg )}^{n} } \\ \\ ⇛\sf {\dfrac{12100}{10000} = {\Bigg ( \dfrac{11}{10} \Bigg )}^{n} } \\ \\ ⇛\sf {\dfrac{121}{100} = {\Bigg ( \dfrac{11}{10} \Bigg )}^{n} } \\ \\⇛ \sf { {\Bigg ( \dfrac{11}{10} \Bigg )}^{2} } \: = \: { {\Bigg ( \dfrac{11}{10} \Bigg )}^{n} } \\ \\ \sf \: as \: the \: Base \: is \: equal \\ \sf \: So, \: the \: another \: power \: must \: be \: equal \: too \\ \sf \: ⇛{ therefore \: the \: answer \: is} \: \: \large{ \underline{ \red {2 = n }}} \\ \\ \: \: \: \: \: \: \: \: \: \: \huge \sf{@WildCat7083 }$