If simple interest and compound interest of a certain sum of money for

1.	If simple interest and compound interest of a certain sum of money for two years are RS. 8400 and RS. 8652 ,then find the sum of money and the rate of interest.
Answer» $\sf\small\underline{Let:-}$ $\tt{\implies The\:sum\:of\: money=P}$ $\tt{\implies The\:rate\:of\: interest=r}$ $\sf\small\underline{To\: Find:-}$ $\tt{\implies The\:sum\:and\:rate=?}$ $\sf\small\underline{Solution:-}$ To CALCULATE the sum and rate at first we have to set up equation by applying formula of simple interest and compound interest with the help of GIVEN clue. $\rm\large\underline{Calculation\:for\:SI:-}$ $\tt\small\underline{Sum=P\:\:T=2years\:\:R=r\:\:SI=Rs.8400:-}$ $\tt{\longrightarrow SI=\dfrac{PTR}{100}}$ $\tt{\longrightarrow 8400=\dfrac{P2R}{100}}$ $\tt{\longrightarrow 2Pr=840000}$ $\tt{\longrightarrow Pr=420000-----(i)}$ $\rm\large\underline{Calculation\:for\:CI:-}$ $\tt\small\underline{Sum=P\:\:T=2years\:\:R=r\:\:CI=Rs.8652:-}$ $\tt{\longrightarrow CI=P\bigg[1+\dfrac{r}{100}\bigg]^n-P}$ $\tt{\longrightarrow 8652=P\bigg[1+\dfrac{r}{100}\bigg]^2-P}$ $\tt{\longrightarrow 8652=P\bigg[\dfrac{100+r}{100}\bigg]^2-P}$ $\tt{\longrightarrow 8652=P\bigg[\dfrac{10000+200r+r^2}{10000}\bigg]-P}$ $\tt{\longrightarrow 8652=\dfrac{10000P+200Pr+Pr^2}{10000}-P}$ $\tt{\longrightarrow 8652=\dfrac{10000P+200Pr+Pr^2-10000P}{10000}}$ $\tt{\longrightarrow 865210000=200Pr+Pr^2}$ $\tt{\longrightarrow 865210000=Pr(200+r)----(ii)}$ Substituting the value of Pr = 420000 :-] $\tt{\longrightarrow 8652*10000=420000(200+r)}$ $\tt{\longrightarrow 8652=42(200+r)}$ $\tt{\longrightarrow (200+r)=8652\div\:42}$ $\tt{\longrightarrow 200+r=206}$ $\tt{\longrightarrow r=206-200}$ $\tt{\longrightarrow r=6\%}$ PUTTING the value of r=6 in eq (i):-] $\tt{\longrightarrow Pr=420000}$ $\tt{\longrightarrow P(6)=420000}$ $\tt{\longrightarrow P=70000}$ $\sf\large{Hence,}$ $\tt\red{\implies The\:sum\:of\: money=Rs.70000}$ $\tt\blue{\implies The\:rate\:of\: interest=6\%}$

If simple interest and compound interest of a certain sum of money for two years are RS. 8400 and RS. 8652 ,then find the sum of money and the rate of interest.

Answer»

$\sf\small\underline{Let:-}$

$\tt{\implies The\:sum\:of\: money=P}$

$\tt{\implies The\:rate\:of\: interest=r}$

$\sf\small\underline{To\: Find:-}$

$\tt{\implies The\:sum\:and\:rate=?}$

$\sf\small\underline{Solution:-}$

To CALCULATE the sum and rate at first we have to set up equation by applying formula of simple interest and compound interest with the help of GIVEN clue.

$\rm\large\underline{Calculation\:for\:SI:-}$