Question

find the difference between compound interest and simple interest on Rs 45000 at 12 % per annul for 3years​

Answer 1

$\huge{\red{\underline{\rm{Solution:}}}}$

${\blue{\underline{\sf{Given:}}}}$

$\sf{\implies Principal\;amount\;(P)=Rs.\;45,000}$

$\sf{\implies Rate\;of\;interest\;(r)=12\%}$

$\sf{\implies Time\;(t)=3\;years}$

${\blue{\underline{\sf{To\;Find:}}}}$

$\sf{\implies Difference\;between\;compound\;interest\;(CI)\;and\;simple\;interest\;(SI).}$

${\blue{\underline{\sf{Formula\;used:}}}}$

$\sf{\implies Compound\;interest\;(CI)=\Bigg[P\Bigg(1+\dfrac{r}{100}\Bigg)^{t}-1\Bigg]}$

$\sf{\implies Simple\;interest\;(SI)=\dfrac{PRT}{100}}$

$\green{\underline{\sf{Now,\;firstly\;we\;will\;calculate\;compound\;interest\;(CI).}}}$

$\sf{\implies Compound\;interest\;(CI)=\Bigg[P\Bigg(1+\dfrac{r}{100}\Bigg)^{t}-1\Bigg]}$

$\sf{\implies CI=\Bigg[45000\Bigg(1+\dfrac{12}{100}\Bigg)^{3}-1\Bigg]}$

$\sf{\implies CI=\Bigg[45000\Bigg(\dfrac{112}{100}\Bigg)^{3}-1\Bigg]}$

$\sf{\implies CI=\Bigg[45000\Bigg(\dfrac{1404928}{1000000}-1\Bigg)\Bigg]}$

$\sf{\implies CI=\Bigg[45000\Bigg(\dfrac{1404928-1000000}{1000000}\Bigg)\Bigg]}$

$\sf{\implies CI=45000\Bigg[\dfrac{404928}{1000000}\Bigg]}$

$\sf{\implies CI = 45000 \times 0.404928}$

$\large{\boxed{\boxed{\purple{\sf{\implies CI=Rs.\;18,221.76}}}}}$

$\green{\underline{\sf{Now,\;We\;will\;calculate\;simple\;interest\;(SI).}}}$

$\sf{\implies Simple\;interest\;(SI)=\dfrac{PRT}{100}}$

$\sf{\implies SI=\dfrac{45000\times 12\times 3}{100}}$

$\sf{\implies SI=\dfrac{1620000}{100}}$

$\large{\boxed{\boxed{\purple{\sf{\implies SI=Rs.\;16200}}}}}$

${\green{\underline{\sf{Now,\;Difference\;between\;CI\;and\;SI\;is,}}}}$

$\sf{\implies Difference=CI-SI}$

$\sf{\implies Difference=18,221.76-16,200}$

$\huge{\boxed{\boxed{\red{\sf{\implies Difference=Rs.\;2,021.76}}}}}$

Answer 2

AnswEr :

• Principal = Rs. 45,000
• Rate = 12% p.a.
• Time = 3 Years

$\leadsto\sf{Difference = Compound \: Interest - Simple \: Interest}$

$\leadsto\sf{Diff. = \bigg[P \bigg(1 + \dfrac{r}{100} \bigg)^{t} - 1 \bigg]- \bigg[\dfrac{PRT}{100} }\bigg]$

• Plugging the Values

$\leadsto\sf{Diff. = \bigg[45000 \bigg(1 + \cancel\dfrac{12}{100} \bigg)^{3} - 1 \bigg]- \bigg[\dfrac{450 \cancel{00} \times 12 \times 3} {\cancel{100}} } \bigg]$

$\leadsto\sf{Diff. = \bigg[45000 \bigg(1 + \dfrac{3}{25} \bigg)^{3} - 1 \bigg]- \bigg[450 \times 12 \times 3 } \bigg]$

$\leadsto\sf{Diff. = \bigg[45000 \bigg( \dfrac{28}{25} \bigg)^{3} - 1 \bigg]- 16200}$

$\leadsto\sf{Diff. = \bigg[45000 \bigg( \dfrac{21952}{15625} - 1\bigg) \bigg]- 16200}$

$\leadsto\sf{Diff. = \bigg( \cancel{45000} \times \dfrac{6327}{ \cancel{15625}} \bigg) - 16200}$

$\leadsto\sf{Diff. =(2.88 \times 6327) - 16200}$

$\leadsto\sf{Diff. =18,221.76 - 16,200}$

$\leadsto\sf{Diff. =Rs. \: 2,021.76}$

⠀

$\therefore$ Diff. betwⁿ CI and SI is Rs. 2,021.76