what is the difference between simple interest and compound interest for 2 years at the rate of 5 percent on RS.1000?​

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1. Given :-

   • Principal = ₹1000
   • Time = 2 years
   • Rate% = 5%

   Aim :-

   • To find the difference between Compound interest and Simple interest

   Simple interest :-

   Formula to use :-

   [tex]\longrightarrow \sf Simple \: interest = \dfrac{Principal \times Rate \times Time}{100}[/tex]

   Substituting the values,

   [tex]\implies \sf Simple\: Interest = \dfrac{1000 \times 5 \times 2}{100}[/tex]

   Cancelling,

   [tex]\implies \sf Simple \: interest = \dfrac{10\not0\not0 \times 5 \times 2}{1\not0\not0}[/tex]

   [tex]\implies \sf Simple \: interest = 10 \times 5 \times 2[/tex]

   [tex]\implies \sf Simple \: interest = 100[/tex]

   Compound interest :-

   In order to find the compound interest, we first have to find the amount.

   Formula to use :-

   [tex]\longrightarrow \sf Amount = Principal\bigg( 1 + \dfrac{rate\%}{100} \bigg)^{time}[/tex]

   [tex]\longrightarrow \sf Compound \: interest = (Amount) – (Principal)[/tex]

   Substituting the values,

   [tex]\implies \sf Amount = 1000\bigg(1 + \dfrac{5}{100} \bigg)^{2}[/tex]

   Taking LCM = 100,

   [tex]\implies \sf Amount = 1000\bigg(\dfrac{100 + 5}{100} \bigg)^{2}[/tex]

   [tex]\implies \sf Amount = 1000\bigg(\dfrac{105}{100} \bigg)^{2}[/tex]

   Reducing the fraction to the lowest terms,

   [tex]\implies \sf Amount = 1000\bigg(\dfrac{21}{20} \bigg)^{2}[/tex]

   [tex]\implies \sf Amount = 1000 \times \dfrac{21}{20} \times \dfrac{21}{20}[/tex]

   [tex]\implies \sf Amount = 10\not0\not0 \times \dfrac{21}{2\not0} \times \dfrac{21}{2\not0}[/tex]

   Reducing to the lowest terms,

   [tex]\implies \sf Amount = 5 \times 21 \times \dfrac{21}{2}[/tex]

   [tex]\implies \sf Amount = 1102.5[/tex]

   Now that we have the value of the Amount, the compound interest will be :-

   [tex]\implies \sf 1102.5 – 1000[/tex]

   [tex]\implies \sf 102.5[/tex]

   Difference :-

   The difference between the compound interest and the simple interest will be :-

   [tex]\implies \sf 102.5 – 100[/tex]

   [tex]\implies \sf 2.5[/tex]

   Therefore the difference is ₹2.5

   Some more formulas :-

   • When interest is compounded half yearly :-

   [tex]\longrightarrow \sf Amount = Prinicipal\bigg(1 + \dfrac{rate\%}{200} \bigg)^{2\times time}[/tex]

   • When the interest is compounded quarterly :-

   [tex]\longrightarrow \sf Amount = Prinicipal\bigg(1 + \dfrac{rate\%}{400} \bigg)^{4 \times time}[/tex]

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