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

Answer:

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

Need To Find :-

Difference between CI and SI.

Solution :-

As we know that

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

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

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

$\frak \pink{SI = 400}$

Now,

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

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

$\large \sf \: Amount \: = \bigg(4000 \bigg \lgroup \dfrac{100 + 5}{100} \bigg \rgroup \bigg) {}^{2}$

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

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

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

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

$\large \sf \: Amount = 4410$

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

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

$\frak \pink{CI = 441}$

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

$\large \sf Difference = 441 - 400$

$\large \sf Difference = 41$

Answer 2

◑ Given ◐

• Principal (P) = Rs.4000

• Rate of interest (R) = 5%

• Time (T or n) = 2 years

◑ To find ◐

Difference between compound interest and simple interest

◑ Solution ◐

$\\\qquad \large{\underline{\mathfrak{\red{\quad \star \: According\:to\:the\:question \: \star \quad}}}}$

Formula of Simple Interest

$\\\implies{\bf{\green{Simple\:interest = \dfrac{P\times R\times T}{100}}}}$

• Substitute the values of P, R & T

$\\\implies\sf S.I = \dfrac{4000\times 5\times 2}{100}$

$\implies\sf S.I = 40\times 5\times 2$$\implies\sf S.I = Rs.400$

$\therefore{\underline{\boxed{\sf{Simple\: interest = Rs.400}}}}$

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$\\\implies{\bf{\green{Amount = P \bigg(1 + \dfrac{R}{100}\bigg)^n}}}$

• Substitute the values of P, R & n

$\\\implies\sf Amount = 4000 \bigg(1 + \dfrac{5}{100}\bigg)^2$

$\implies\sf Amount = 4000 \bigg(1 + \dfrac{1}{20}\bigg)^2$

$\implies\sf Amount = 4000 \bigg(\dfrac{20 + 1}{20}\bigg)^2$

$\implies\sf Amount = 4000 \bigg(\dfrac{21}{20}\bigg)^2$

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

$\implies\sf Amount = 10\times 21 \times 21$

$\implies\sf Amount = Rs.4410$

• As we know that

$\\\implies{\bf{\green{Compound\: interest = Amount - Principal}}}$

$\implies\sf C.I= 4410 - 4000$

$\implies\sf C.I= 441$

$\therefore{\underline{\boxed{\sf{Compound\: Interest= Rs.441}}}}$

• We have to find difference between compound interest and simple interest

$\\\implies{\bf{\green{Compound\: interest - Simple\: interest}}}$

$\implies\sf 441 - 400$$\implies\sf Rs.41$

${\underline{\sf{\purple{The\:difference\:between\:S.I\:and\:C.I\:is\: \bf Rs.41}}}}$

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