Question

Find the compound interest on Rs. 12000 for 3 years at 10% per annum compounded
annually.​

Answer 1

Answer:

Step-by-step explanation:

We know that the amount A at the end of n years at the rate of R % per annum when the interest is compounded annually is given by A=P(1+  100 R  )  n

 

Here P = Rs.12000 R = 10% per annum and n = 3

∴ Amount after 3 years = P(1+  100 R  )3

=Rs.12000×(1+  

100 10  )  3  =Rs.12000×(1+  10 1 ) 3

 

=Rs.12000×(  10 11  )  3  =Rs.12000×  10 11  ×  10 11  ×  10 11

​   =Rs.(12×11×11×11)=Rs.15972

Now Compound interest = A - P ⇒ Compound interest = Rs. 15972 - Rs.12000 = Rs. 3972

Answer 2

$\bf \: \underline{ Given }\: :$ ↴

$\sf \: Principal \: : \: Rs. 12000$

$\sf \: Time \: : \: 2 \: Years$

$\sf \: Rate \: of \: Interest \: : \: 10 \%$

$\bf \: \underline{To \: find }\: :$ ↴

$\sf \: We \: have \: to \: find \: the \: Compound \: Interest.$

$\sf \: \bigstar \underline{\: So, \: Let's \: Start \: } \bigstar$

$\sf \: First \: of \: all \: we \: are \: going \: to \: find \: the \: amount..$

$\green{ \underline{\boxed{ \sf \: Amount \: : P \: \bigg(\: 1 + \frac{R}{100} \: \bigg ) ^{n} }}}$

$\sf \: Putting \: the \: value \: into \: the \: formula :$

$\sf \: Amount \: : 12000 \: \bigg(\: 1 + \dfrac{10}{100} \: \bigg ) ^{3}$

$\sf \: \underline{Add \: 1 \: and \: 10.}$

$\sf \: Amount \: : 12000 \: \bigg(\: \dfrac{11}{10} \bigg ) ^{3}$

$\sf \: Amount \: \rightarrow \: 12000 \: \bigg( \: \dfrac{11}{10} \: \times \: \dfrac{11}{10} \: \times \dfrac{11}{10} \bigg)$

$\sf \: \underline{Simplify \: the  \: expression.}$

$\sf \: Amount \: \rightarrow \: 12000 \: \bigg(\dfrac{1331}{1000} \bigg)$

$\sf \: Cancel \: the  \: common \: factor  \: of  \: 1000.$

$\sf \: Amount \: \rightarrow \: 12000 \: \times \: 1331$

$\sf \: \underline{Multiply  \: 1212  \: b y  \: 1331}$

$\purple{ \sf \: Amount \: \rightarrow \: 12000 \: \times \: 1331 \: = \: Rs. \: 15972 \: \star}$

$\sf \: Now, \: we \: will \: find \: the \: Compound \: Interest..$

$\green{ \underline{\boxed {\sf \: CI \: = \: Amount \: - \: Principal}}}$

$\sf \: CI \: = \: 15972 \: - \: 12000$

$\purple{\sf \: CI \: = \: Rs. \: 3972 \:\star}$