Question

what is the difference between simple interest and compound interest for 2 years at the rate of 5% and rupees 1000​

Answer 1

Given : ↴

$\sf \: Principal \: = \: Rs. \: 1 000$

$\sf \: Time \: : \: 2 \: years$

$\sf \: Rate \: of \: Interest \: : 5 \: \%$

To find : ↴

We have to find the difference between simple interest and compound interest.

So, Let's find it : ↴

$\sf \:So,\: first\: of \:all \:We \:will\: found\: the \:Compound \:Interest.$

$\sf \: Formula \: to \: find \: Amount \: is \: :$ ↴

$\sf \: \red{Amount }\: = \: \blue{Principal \ \bigg[ 1 \: + \: \dfrac{Rate}{100} \bigg] ^{Time} }$

$\sf \: Amount \: = \: 1000 \ \bigg[ 1 \: + \: \dfrac{5}{100} \bigg] ^{2}$

$\sf \: Amount \: = \: 1000 \ \bigg[ 1 \: + \: \dfrac{1}{20} \bigg] ^{2}$

$\sf \: Amount \: = \: 1000 \ \bigg[ \: \dfrac{20 \: + 1}{20} \bigg] ^{2}$

$\sf \: Amount \: = \: 1000 \ \bigg[ \: \dfrac{21}{20} \bigg] ^{2}$

$\sf \: Amount \: = \: 1000 \ \: \times \: \dfrac{21}{20} \: \times \: \dfrac{21}{20}$

$\sf \: Amount \longrightarrow \: 1000 \: \times \: \dfrac{21}{20} \: \times \: \dfrac{21}{20} \: = \: 1102.5$

$\bf \: So, \: Amount \: = \: Rs. \: 1102.5$

$\boxed{ \sf \: C.l = Amount - Principal }$

$\sf \: C.I \: \longrightarrow \: 1102.5 \: - \: 1000 \: = \: Rs. \: 102.5$

$\sf\: \underline{Now \: We \: will \: find \: the\: SI.}$

$\sf \: Formula \: used \: to \: find \: S I :$ ↴

$\sf \: \red{Simple \: Interest} = \blue{\dfrac{\: P \: \times R \times \: T }{100} }$

$\sf \: Simple \: Interest : \dfrac{\: 1000 \: \times 5 \times \: 2 }{100}$

$\sf \: Simple \: Interest : Rs.\: 100$

$\sf \: So, \: Difference \: between \: CI \: and \: SI \: = \: 102.5 \: - \: 100$

$\bf \: 102.5 \: - \: 100 \: = \: 2.5$

$\sf \purple{ \sf \: So, \: Difference \: between \: them \: is \: Rs. \: 2.5}$