Question

find the difference between compound interest and simple interest on a sum of rupees 12000 @ 12% per annum for 2 years​

Answer 1

AnswEr :

$\bf{Given}\begin{cases}\sf{Principal = Rs. \:12000}\\\sf{Rate=12\%\:p.a.}\\ \sf{Time=2 \:Years}\\\text{Find Difference between CI and SI} \end{cases}$

• Let's Head to the Question Now :

$\implies\tt{Difference = Compound \:Interest - Simple \:Interest} \\ \\\implies\tt{Diff. = \bigg[P \bigg(1 + \dfrac{r}{100} \bigg)^{t} -1 \bigg]- \bigg[\dfrac{PRT}{100} }\bigg] \\ \\\implies\tt{Diff. = \bigg[12000 \bigg(1 + \cancel\dfrac{12}{100} \bigg)^{2} - 1 \bigg]- \bigg[\dfrac{120 \cancel{00} \times12 \times2}{\cancel{100}} }\bigg] \\ \\\implies\tt{Diff. = \bigg[12000 \bigg(1 + \dfrac{3}{25} \bigg)^{2} - 1 \bigg]- \bigg[120 \times12 \times2\bigg]}\\ \\\implies\tt{Diff. = \bigg[12000 \bigg(\dfrac{28}{25} \bigg)^{2} - 1\bigg]- \bigg[1440 \times2\bigg]} \\ \\\implies\tt{Diff. = \bigg[12000 \bigg(\dfrac{784}{625} - 1 \bigg) \bigg]- 2880} \\ \\\implies\tt{Diff. = \bigg[12000 \times\dfrac{159}{625}\bigg]- 2880} \\ \\\implies\tt{Diff. = \bigg[19.2 \times 159\bigg]- 2880} \\ \\\implies\tt{Diff. = Rs. \:(3052.8 - 2880)} \\ \\\implies \large\boxed{\tt{Diff. =Rs. \:172.8}}$

⠀

∴ Difference b/w CI and SI is Rs. 172.8

$\rule{300}{2}$

• S H O R T C U T ⠀T R I C K :

$\longrightarrow \tt Difference = \dfrac{P {r}^{2}}{(100)^{2}} \\ \\\longrightarrow \tt Difference = \dfrac{12\cancel{000} \times {12}^{2} }{10 \cancel{000}}\\ \\\longrightarrow \tt Difference =\dfrac{12 \times 144}{10} \\ \\\longrightarrow \tt Difference =\dfrac{1728}{10} \\ \\\longrightarrow \large \boxed{\tt Difference = Rs. \: 172.8}$

⠀

∴ Difference b/w CI and SI is Rs. 172.8

◗ NOTE : This Shortcut Trick is only Applicable for 2 Years Interest.

#answerwithquality #BAL

Answer 2

$\huge{\red{\underline{\mathfrak{Answer = Rs.172.8}}}}$

$\underline{\huge{\underline{\purple{Given}}}}$

Principal = Rs 2000

Rate = 12% p.a.

Time = 2 Years

$\underline{\huge{\mathcal{\purple{To\;find:}}}}$

The difference between compound interest and simple interest.

Solution steps

$\rightarrow\textbf{Difference = Compound \:Interest - Simple \:Interest} \\ \\\rightarrow\bold{Diff. = \bigg[P \bigg(1 + \dfrac{r}{100} \bigg)^{t} -1 \bigg]- \bigg[\dfrac{PRT}{100} }\bigg] \\ \\\rightarrow\bold{Diff. = \bigg[12000 \bigg(1 + \cancel\dfrac{12}{100} \bigg)^{2} - 1 \bigg]- \bigg[\dfrac{120 \cancel{00} \times12 \times2}{\cancel{100}} }\bigg] \\ \\\rightarrow\bold{Diff. = \bigg[12000 \bigg(1 + \dfrac{3}{25} \bigg)^{2} - 1 \bigg]- \bigg[120 \times12 \times2\bigg]}\\ \\\rightarrow\bold{Diff. = \bigg[12000 \bigg(\dfrac{28}{25} \bigg)^{2} - 1\bigg]- \bigg[1440 \times2\bigg]} \\ \\\rightarrow\bold{Diff. = \bigg[12000 \bigg(\dfrac{784}{625} - 1 \bigg) \bigg]- 2880} \\ \\\rightarrow\bold{Diff. = \bigg[12000 \times\dfrac{159}{625}\bigg]- 2880} \\ \\\rightarrow\bold{Diff. = \bigg[19.2 \times 159\bigg]- 2880} \\ \\\rightarrow\bold{Diff. = Rs. \:(3052.8 - 2880)} \\ \\\rightarrow \large{\bold{Diff. =Rs. \:172.8}}$