Question

Difference between si and ci for 3 years formula

Answer 1

Step-by-step explanation:

If a principal amount is given, then it is possible to find the difference between the SI fetch on the given principal for 2 yrs and the CI fetch on the same principal for 2 yrs at the same rate of interest .

Answer 2

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$\green{\textbf{Difference between ci and si for 3 years formula deriviation.}}$

$\Large\bold\star\underline{\underline\textbf{Formula\:used}}$

• CI = A - P where A = $\tiny\red{\boxed{\sf A\:=\:P( 1 + \frac{r}{100})^{t}}}$

• SI = (P×R×T)/100

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Let ,

D = CI for 3 years - SI for 3 year ,

$\textbf{ Putting values we get,,}$

$\begin{lgathered}\green{\red \leadsto D = [P(1 + \frac{r}{100})^{3} - P] - ( \frac{P \times r \times 3}{100})} \\ \\ \green{ \red \leadsto D =P( \frac{(100 + r)^{3} }{ {100}^{3}} - 1) - \frac{3Pr}{100}} \\ \\ \green{\red \leadsto D = P[ \frac{(100 + r)^{3} - {100}^{3} }{ {100}^{3} } - \frac{3r}{100}]} \\ \\\bf\:using , \orange{\large\boxed{\bold{( {x}^{3} - {y}^{3} ) = (x - y)( {x}^{2} + {y}^{2} + xy)}}} \\ \\ \red \leadsto \pink{D =P[ \frac{(100 + r - 100)( {100}^{2} + {r}^{2} + {100}^{2} + {100}^{2} + 300r) }{ {100}^{3} } - \frac{3r}{100}]} \\ \\ \red \leadsto \pink{D =P[ \: \frac{r(3 \times {100}^{2} + 300r + {r}^{2}) }{ {100}^{3} } - \frac{3r}{100}]} \\ \\ \red \leadsto \blue{D =P[ \: \frac{3r {100}^{2} + 300 {r}^{2} + {r}^{3} - 3r {100}^{2} }{100^{3} } ]} \\ \\ \red \leadsto D =P[ \: \frac{ {r}^{3} + 300 {r}^{2} }{ {100}^{3} } ] \:\end{lgathered}$

$\textbf{Or, we can Learn it As,,}$

$\red{\large\boxed{\bold{D = P( \frac{r}{100} )^{2}( \frac{r}{100} + 3)}}}$

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The above formula is applicable only in the following conditions::----

1. The principal in simple interest and compound interest must be same.

2. Rate of interest must be same in simple interest and compound interest.

3. In compound interest, interest has to be compounded annually.

$\large\underline\textbf{Hope it Helps You.}$

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