Q26)Find the compound
interest on Rs60,000 at the rate
of 10% per annum for 1.5 years
when interest is compounded

November 29, 2021

By Emery

1 thought on “Q26)Find the compound<br />interest on Rs60,000 at the rate<br />of 10% per annum for 1.5 years<br />when interest is compounded<b”

1. Given :-

   • Principal = ₹60,000
   • Rate = 10%
   • Time = 1.5 years
   • Interest is compounded semi annually (meaning half yearly)

   Aim :-

   • To find the Compound interest on the principal

   Formula to use :-

   In order to find the Compound interest we first have to find the amount

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

   • Compound interest = Amount – Principal

   Answer :-

   Let us substitute the values to find the amount

   • Let amount be A

   [tex]\implies\sf{A} = 60000\bigg(1+\dfrac{10}{200} \bigg)^{2\times1.5}[/tex]

   By taking the LCM,

   [tex]\implies\sf{A} = 60000\bigg(\dfrac{200+10}{20}\bigg)^{3}[/tex]

   By adding,

   [tex]\implies\sf{A} = 60000\bigg(\dfrac{210}{200} \bigg)^{3}[/tex]

   By reducing to the lowest terms,

   [tex]\implies \sf{A} = 60000\bigg(\dfrac{21}{20} \bigg)^{3}[/tex]

   [tex]\implies \sf{A} = 60000 \times \dfrac{21}{20} \times \dfrac{21}{20} \times \dfrac{21}{20}[/tex]

   By cancelling, we get :-

   [tex]\implies \sf{A} = 69457.5[/tex]

   Therefore,

   • Amount = ₹69457.5

   Now that we have the value of the Amount and the Principal,

   Compound interest :-

   [tex]\implies 69457.5 – 60000[/tex]

   [tex]\implies 9457.5[/tex]

   Some more formulas :-

   • When interest is compounded Annually :-

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

   • When interest is compounded quarterly :-

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

   • Simple interest :-

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

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