Question

Compute the amount and the compound interest in each of the following by using the
formulae when
Principal - Rs 5000, Rate = 10 paise per rupee per annum, Time = 2 years​

Answer 1

AnSwer :

$\frak {\pink{Given}}\begin{cases} \frak{\green{Principal=Rs.5000}}\\ \frak{\blue{Time=2\:Years}}\\ \frak{\orange{Rate=10\%}}\\ \frak{\red{Amount= \: ?}}\\ \frak{\gray{Compound \: Interest = \: ?}}\end{cases}$

We have to calculate the amount and compound interest. So, first we will calculate the amount by using given below formula :

$:\implies\:\sf Amount = P \Bigg\lgroup 1 + \dfrac{R}{100} \Bigg\rgroup^{n}$

Where,

• A = Amount
• P = Principal
• R = Rate
• n = Time

Now, simply just plug in the known values in above formula we get :

$:\implies\:\sf Amount = 5000 \Bigg\lgroup 1 + \dfrac{10}{100} \Bigg\rgroup^{2}$

$:\implies\:\sf Amount = 5000 \Bigg\lgroup 1 + \dfrac{1}{10} \Bigg\rgroup^{2}$

$:\implies\:\sf Amount = 5000 \Bigg\lgroup \dfrac{10 + 1}{10} \Bigg\rgroup^{2}$

$:\implies\:\sf Amount = 5000 \Bigg\lgroup \dfrac{11}{10} \Bigg\rgroup^{2}$

$:\implies\:\sf Amount = 5000 \times \dfrac{121}{100}$

$:\implies\:\sf Amount = 50 \times 121$

$:\implies\: \underline{ \boxed{\sf Amount =Rs. \: 6050}}$

• Hence,the amount is Rs. 6050

Now, let's find the Compound Intrest :

$\dashrightarrow\:\:\sf Compound \: Intrest = Amount - Principal$

$\dashrightarrow\:\:\sf Compound \: Intrest = 6050 - 5000$

$\dashrightarrow\:\: \underline{ \boxed{\sf Compound \: Intrest =Rs. \: 1050}}$

• Hence, the Compound Intrest is Rs. 1050.

$\boxed{\begin{minipage}{5cm}\bigstar \:\underline{\textbf{Profit and Loss Formulas :}}\\\\ \\ \sf{\textcircled{\footnotesize\textsf{1}}}S.P. = \sf \bigg\lgroup\dfrac{100 + Profit \%}{100}\bigg\rgroup \times 100 \\\\\\ \sf {\textcircled{\footnotesize\textsf{2}}}\:C.P. = \sf \dfrac{S.P. \times 100}{100 + Profit \%} \\\\\\\sf{\textcircled{\footnotesize\textsf{3}}}\:Profit = \sf \dfrac{Profit \% \times C.P.}{100} \\\\\\ \sf{\textcircled{\footnotesize\textsf{4}}}Profit (gain) = S.P. - C.P. \\\\\\\sf{\textcircled{\footnotesize\textsf{5}}}\: \sf Profit \% = \dfrac{Profit}{C.P.} \times 100 \end{minipage}}$

Answer 2

$\boxed{\huge{\bf{\star{Correct\:question \:-:}}}}$

• Compute the amount and the compound interest in each of the following by using the formulae when ,
• Principal - Rs 5000, Rate = 10 %, Time = 2 years.

AnswEr-:

• $\boxed{\sf{\large { Amount =\:Rs.\:6050 }}}$

• $\boxed{\sf{\large { Compound \:Interest\:=\:Rs.1050 \: }}}$

$\dag{\sf{\large { EXPLANATION:\:}}}$

• $\frak{Given \:\: -:} \begin{cases} \sf{Principal= \frak{Rs.5000}} & \\\\ \sf{Rate \:=\:\frak{10\%}}& \\\\ \sf{Time \:=\:\frak{2 \ year}}\end{cases}$

• $\frak{To \:Find\: -:} \begin{cases} \sf{The\:Amount, \: and, } & \\\\ \sf{The\:Compound\:Interest. }\end{cases}$

$\dag{\sf{\large { Solution-:\:}}}$

• $\implies{\sf{\large { Amount \: =P\left(1 \: +\dfrac{R}{100} \right)^{n}}}}$

• $\frak{Here \:\: -:} \begin{cases} \sf{P \:= \:Principal\:= \frak{Rs.5000}} & \\\\ \sf{R\:=Rate \:=\:\frak{10\%}}& \\\\ \sf{n \: = Time \:=\:\frak{2 \ year}}& \\\\ \sf{A\:=Amount \:=\:\frak{??}}\end{cases}$

$\dag{\sf{\large { Now,\:Substitute \:the\:Known\:value\:in\:Formula.-: }}}$

• $\implies{\sf{\large { Amount \: =5000 \left(1 \: +\dfrac{10}{100} \right)^{2}}}}$

• $\star{\sf{\large { Or,\:}}}$

• $\implies{\sf{\large { Amount \: =5000\left(\dfrac{1}{1} \: +\dfrac{10}{100} \right)^{2}}}}$

• $\implies{\sf{\large { Amount \: =5000\left(\dfrac{1}{1} \: +\dfrac{1}{10} \right)^{2}}}}$

• $\implies{\sf{\large { LCM \:of\:10\:and\:1\:is = \:10}}}$

• $\implies{\sf{\large { Amount \: =5000\left( \: \dfrac{10+1}{10} \right)^{2}}}}$

• $\implies{\sf{\large { Amount \: =5000\left( \: \dfrac{11}{10} \right)^{2}}}}$

• $\implies{\sf{\large { 11^{2} = \:121\:and\:,\:10^{2}= 100}}}$

• $\implies{\sf{\large { Amount \: =5000 \times \dfrac{121}{100} }}}$

• $\implies{\sf{\large { Amount \: =50 \times 121 }}}$

• $\implies{\sf{\large { Amount =\:Rs.\:6050 }}}$

$\star{\sf{\large { Therefore-:\:}}}$

• $\boxed{\sf{\large { Amount =\:Rs.\:6050 }}}$

$\star{\sf{\large { Now-:\:}}}$

• $\implies{\sf{\large { Compound \:Interest\:=\:Amount \:- Principal }}}$

• $\frak{Here\: -:} \begin{cases} \sf{\:Amount=\:Rs.6050 \: and, } & \\\\ \sf{Principal\:=Rs.5000 }\end{cases}$

$\star{\sf{\large { Now-:\:}}}$

• $\implies{\sf{\large { Compound \:Interest\:=\:6050 \:- 5000 }}}$

• $\implies{\sf{\large { Compound \:Interest\:=\:1050 \: }}}$

$\star{\sf{\large { Therefore-:\:}}}$

• $\boxed{\sf{\large { Compound \:Interest\:=\:1050 \: }}}$

$\star{\sf{\large { Hence:\:}}}$

• $\boxed{\sf{\large { Amount =\:Rs.\:6050 }}}$

• $\boxed{\sf{\large { Compound \:Interest\:=\:Rs.1050 \: }}}$

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