Math, asked by memontouhid212, 9 days ago

find the compound interest at the end of 1 year on 10,000 at the rate of 8% per annum interest is compounded half-yearly​

Answers

Answered by Yugant1913
46

Step-by-step explanation:

 \large \dag \underline{  \bf\underline{Given  \: information  :  -  -  - }}

  • ➯ Time = 1 year
  • ➯ Principal = 10,000
  • ➯ Rate Of Interest

\large \dag \underline{  \underline{ \textbf{What we need to calculate  :  -  -  - }}}

  • ➯Compound Interest
  • ➯Amount

 \large \dag \underline{  \bf\underline{ \green{S olution } :  -  -  - }}

  \red\bigstar Here the Interest is Compounded half yearly

↬Time = 1 years

  • Half of 1 year is 6 months

↬Time = 2 half years

 \red \bigstarThe rate of interest is also Compounded half yearly

↬Rate of interest = 8%

↬Rate of interest = 8/2

↬Rate of interest = 4%

 \large \red \bigstar Let us find out The Amount by using formula

 \rightarrow  \green\bigstar \underline{ \boxed{ \bf{Amount =  P \bigg( 1+  \dfrac{ R}{100} \bigg)^{2} }}} {}

Where

  • ➯ P = Principle
  • ➯ T = Time
  • ➯ R = Rate
  • ➯ A = Amount

Now subtracting values in formula

  \\  \\  \sf \: ↠ Amount  = 10000 \bigg(1 +  \frac{4}{100}  \bigg) ^{2}    \\  \\ \\  \\  \sf \: ↠ Amount  =10000 \bigg( \frac{ 100 + 4}{100} \bigg) ^{2} \\  \\ \\  \\   \sf \: ↠ Amount  =10000 \bigg( \frac{104}{100} \bigg) ^{2}  \\  \\ \\  \\  \sf \: ↠ Amount  =100 \cancel{00 }\times  \frac{104}{100 }  \times  \frac{104}{ 1\cancel{00} } \\  \\ \\  \\  \sf \: ↠ Amount  =1 \cancel{00} \times  \frac{104}{ 1\cancel{00}}  \times 104 \\  \\  \\  \\  \sf \: ↠ Amount  =104 \times 104 \\  \\  \\  \\  \\  \large \sf \: ↠   \green\bigstar \underline{ \boxed{ \bf Amount  =10186}}

 \large  \red\bigstarLet us find Compounded interest by using formula

  \green\bigstar\underline {\boxed{ \textbf{ \: Compound Interest = Amount- principal }}}

  • Substituting values

 \\  \\ ↬ \sf \: Compound  \: Interest  = 10816 - 10000 \\  \\  \\  \underline{ \large↬ \bf \: Compound  \: Interest  = 816}

 \rule{72mm}{1mm}

{\large{\underline{\underline{\bf{\green{Learn \: More : -}}}}}} \\ \small\circ{\underline{\boxed{\sf{\red{ Simple \: Interest = \dfrac{P \times R \times T}{100}}}}}} \\ \\  \small\circ{\underline{\boxed{\sf{\red{Amount={P{\bigg(1 + \dfrac{R}{100}{\bigg)}^{T}}}}}}}} \\ \\\small\circ{\underline{\boxed{\sf{\red{Amount = Principle + Interest}}}}}  \\ \\\small\circ{\underline{\boxed{\sf{\red{ Principle=Amount - Interest }}}}} \\ \\ \small\circ{\underline{\boxed{\sf{\red{Principle = \dfrac{Amount\times 100 }{100 + (Time \times Rate)}}}}}}</p><p> \\  \\ \small\circ{\underline{\boxed{\sf{\red{Principle = \dfrac{Interest \times 100 }{Time \times Rate}}}}}} \\  \\ \small\circ{\underline{\boxed{\sf{\red{Rate = \dfrac{Simple \: Interest \times 100}{Principle \times Time}}}}}}

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