Question

find the difference between compound interest and simple interest if principal is rupees 4000 and rate is 5% and number of years is two years​

Answer 1

$\begin{gathered}\sf \: Given \begin{cases} \sf Principal = 4000 \\ \sf \: Rate = 5\% \\ \sf \: Time = 2 \: years \end{cases}\end{gathered}$

Need To Find :-

Difference between CI and SI.

Solution:-

As we know that

$\large\sf\:SI = \dfrac{PRT}{100}$

$\large \sf \: SI = \dfrac{ \cancel{4000} \times 5\times 2}{ \cancel{100}}$

$\large \sf \: SI = 40 \times 5 \times 2$

$\sf\large{SI\:=\:400}$

Now,

$\large \sf \: Amount = \bigg(P + \bigg( 1 + \dfrac{R}{100} \bigg ) \bigg) {}^{N}$

$\large \sf \: SI = \dfrac{ \cancel{4000} \times 5 \times 2}{ \cancel{100}}$

$\large \sf \: Amount = \bigg(4000 \bigg \lgroup1 + \dfrac{5}{100} \bigg \rgroup \: \bigg) {}^{n}$

$\large\sf\: Amount \: = \bigg(4000 \times {\frac{105}{100} \bigg)}^{2}$

$\large \sf \: Amount \: = 4000 \times \dfrac{105}{100}\times \dfrac{105}{100}$

$\large \sf \: Amount = 4000 \times \dfrac{21}{20} \times \dfrac{21}{20}$

$\large \sf \: Amount \: = \dfrac{1764000}{400}$

$\sf\large{Amount\:=\:4410}$

$\sf\large{CI\: =\: A\: -\: P}$

$\sf\large{CI\: =\:4410\: -\: 4000}$

$\sf\large{CI\: =\:441}$

$\sf\large{Difference\:=CI\:-SI}$

$\sf\large{Difference\:=441\:-400}$

$\sf\large{Difference\:=41}$