Question

The difference between simple and compound interest on a sum of Rs. 6250 for 3 years is Rs. 193.75. What is the rate ? ​

Answer 1

$\large{\underline{\frak{\pmb{Given ...}}}}$➣ Principle = Rs.6250➣ Time = 2 years➣ Rate = 4 p.c.p.a.$\large{\underline{\frak{\pmb{To \:Find ...}}}}$➣ Simple Interest➣ Compound Interest➣ Difference between Interests$\large{\underline{\frak{\pmb{Using \: Formula ...}}}}$$\odot {\underline{ \boxed{\sf{S.I= \dfrac{P \times R \times T}{100}}}}}$$\odot{\underline{ \boxed{\sf{C.I={P \bigg( 1 + \dfrac{R}{100} { \bigg)}^{T}- P}}}}}$⊙$\small\sf\fbox{Difference = C.I - S.I}$Where➠ S.I = Simple Interest➠ C.I = Compound Interest➠ P = Principle➠ R = Rate➠ T = Time$\large{\underline{\frak{\pmb{Solution...}}}}$$\bigstar \: \textbf \red{Finding\:The\: Simple\: Interest }$$: \implies{\sf{S.I= {\bf{ \dfrac{P \times R \times T}{100}}}}}$Substituting the values$: \implies{\sf{S.I= {\bf{ \dfrac{6250 \times4 \times 2 }{100}}}}}$$: \implies{\sf{S.I= {\bf{ \dfrac{50000}{100}}}}}$$: \implies{\sf{S.I= {\bf{\cancel\dfrac{50000}{100}}}}}$$: \implies{\sf{S.I= {\bf{Rs.500}}}}$$\odot\underline{\boxed{\bf{\purple{S.I={Rs.500}}}}}$The Simple Interest is Rs.500$\bigstar \: \textbf \red{Finding\:The\: Compound\: Interest }$${ : \implies\sf{C.I={\bf{P \bigg( 1 + \dfrac{R}{100} { \bigg)}^{T}- P}}}}$Substituting the values${ : \implies\sf{C.I={\bf{6250 \bigg( 1 + \dfrac{4}{100} { \bigg)}^{2}- 6250}}}}$${ : \implies\sf{C.I={\bf{6250 \bigg(\dfrac{100 + 4}{100} { \bigg)}^{2}- 6250}}}}$${ : \implies\sf{C.I={\bf{6250 \bigg(\dfrac{104}{100} { \bigg)}^{2}- 6250}}}}$${ : \implies\sf{C.I={ \bf{6250 \bigg( \cancel\dfrac{104}{100} { \bigg)}^{2}- 6250}}}}$${ : \implies\sf{C.I={\bf{6250 \bigg( \dfrac{26}{25} { \bigg)}^{2}- 6250}}}}$${ : \implies\sf{C.I={ \bf{6250 \bigg( \dfrac{26}{25} \times\dfrac{26}{25} \bigg){ - 6250}}}}}$${ : \implies\sf{C.I={ \bf{6250 \bigg( \dfrac{676}{625}\bigg){ - 6250}}}}}$${ : \implies\sf{C.I={ \bf{ \bigg(6250 \times \dfrac{676}{625}\bigg){ - 6250}}}}}$${:\implies\sf{C.I={ \bf{ \bigg( \cancel{6250} \times \dfrac{676} {\cancel{625}}\bigg){ - 6250}}}}}$${ : \implies\sf{C.I={ \bf(10 \times {676) - 6250}}}}$${ : \implies\sf{C.I={ \bf{6760 - 6250}}}}$${ : \implies\sf{C.I= \bf{510}}}$$\odot \underline{\boxed{\bf{\purple{C.I={Rs.510}}}}}$The Compound Interest is Rs.510$\bigstar \: \textbf \red{Finding\:The\: Difference\: between\:Interests}$$: \implies{\sf{Difference = \bf{C.I - S.I}}}$Substituting the values$: \implies{\sf{Difference = \bf{510-500}}}$$: \implies{\sf{Difference = \bf{10}}}$$\odot\underline{\boxed{\bf{\purple{Difference = {10}}}}}$Hence forth, The difference between simple interst and compound is Rs.10$\underline\pink{▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬}$

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