Difference between ci and si for 3 years

Asked by admin @ 31/08/2021 in Math viewed by 368 People

Difference between ci and si for 3 years formula deriviation

Answered by admin @ 31/08/2021

AnswEr :

Let's Assume that Principal and Rate is same here with time 3 Years.

• Derivation of Formula Now :

$\leadsto\sf{Difference = Compound \: Interest - Simple \:Interest}$

$\leadsto\sf{Diff. = \bigg[P \bigg(1 + \dfrac{r}{100} \bigg)^{t} - 1\bigg]- \bigg[\dfrac{Prt}{100} }\bigg]$

$\leadsto\sf{Diff. = \bigg[P \bigg(1 + \dfrac{r}{100} \bigg)^{3} - 1 \bigg]- \bigg[\dfrac{Pr\times 3}{100} }\bigg]$

$\leadsto\sf{Diff. = \bigg[P \bigg(\dfrac{100 + r}{100} \bigg)^{3} - 1 \bigg]- \bigg[\dfrac{Pr \times 3}{100} }\bigg]$

$\leadsto\sf{Diff. = \bigg[P \bigg(\dfrac{(100 + r)^{3} }{(100)^{3} } - 1\bigg)\bigg]- \bigg[\dfrac{3Pr}{100} }\bigg]$

$\leadsto\sf{Diff. = \bigg[P \bigg(\dfrac{(100 + r)^{3} - (100)^{3}}{(100)^{3} }\bigg)\bigg]- \bigg[\dfrac{3Pr}{100} }\bigg]$

$\leadsto\sf{Diff. = \bigg[P \bigg(\dfrac{\cancel{(100)^{3}} + {r}^{3} + 300r(100 + r) - \cancel{(100)^{3}}}{(100)^{3} }\bigg)\bigg]- \bigg[\dfrac{3Pr}{100} }\bigg]$

$\leadsto\sf{Diff. = \bigg[P \bigg(\dfrac{ {r}^{3} + 300r(100 + r)}{(100)^{3} }\bigg)\bigg]- \bigg[\dfrac{3Pr}{100} }\bigg]$

$\leadsto\sf{Diff. = P\bigg[ \bigg(\dfrac{ {r}^{3} + 30000r + 300{r}^{2}}{(100)^{3} }\bigg)- \dfrac{3r}{100} }\bigg]$

$\leadsto\sf{Diff.= P\bigg( \dfrac{ {r}^{3} + 30000r + 300{r}^{2} - (3r \times{100}^{2})}{(100)^{3}}} \bigg)$

$\leadsto\sf{Diff.= P\bigg( \dfrac{ {r}^{3} + \cancel{30000r} + 300{r}^{2} - \cancel{30000R}}{(100)^{3}}} \bigg)$

$\leadsto\sf{Diff.= P\bigg( \dfrac{ {r}^{3} + 300{r}^{2}}{(100)^{3}}} \bigg)$

$\leadsto\boxed{\sf{Diff.= P{r}^{2}\bigg( \dfrac{r + 300}{(100)^{3}}} \bigg)}$

Difference between ci and si for 3 years

AnswEr :

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