Find the compound interest on Rs. 1000 for two years at 4% per annuall.​

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1. Answer :–

   • The compound interest is Rs 81.6.

   To find :–

   • The compound interest on Rs 1000 for two years at 4% per annum.

   Solution :–

   • Before finding the compound interest, let’s find the amount!

   We know that :–

   [tex] \underline{ \boxed{\sf Amount = Principal \left(1 + \dfrac{Rate}{100} \right)^{Time}}}[/tex]

   Here,

   • Principal = Rs 1000.
   • Rate = 4% per annum.
   • Time = 2 years.

   Therefore :–

   [tex] \longrightarrow\rm Amount = 1000 \left( 1 + \dfrac{4}{100} \right)^{2} [/tex]

   [tex] \longrightarrow\rm Amount = 1000 \left(1 + \dfrac{1}{25} \right)^{2} [/tex]

   [tex] \longrightarrow\rm Amount = 1000 \left( \dfrac{1 \times 25 + 1 \times 1}{25} \right)[/tex]

   [tex] \longrightarrow\rm Amount = 1000 \left( \dfrac{25 + 1}{25} \right)^{2} [/tex]

   [tex] \longrightarrow\rm Amount = 1000 \left( \dfrac{26}{25} \right)^{2} [/tex]

   [tex] \longrightarrow\rm Amount = 1000 \times \dfrac{26}{25} \times \dfrac{26}{25} [/tex]

   [tex] \longrightarrow\rm Amount = 1000 \times \dfrac{676}{625} [/tex]

   [tex] \longrightarrow\rm Amount = \dfrac{676000}{625} [/tex]

   [tex] \longrightarrow\overline{ \boxed{ \rm Amount = Rs \: 1081.6}}[/tex]

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   • Now, let’s find the compound interest!

   We know that :–

   [tex] \underline{ \boxed{ \sf CI = Amount – Principal}}[/tex]

   Where,

   • CI = Compound Interest.

   Here,

   • Amount = Rs 1081.6.
   • Principal = Rs 1000.

   Therefore,

   [tex] \longmapsto\bf CI = 1081.6 – 1000[/tex]

   [tex] \longmapsto\bf CI = Rs \: 81.6[/tex]

   ________________________________

   Hence :–

   • The compound interest is Rs 81.6.

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