Question

. secretin sum of money at compound interest amount rupees 6600 in years and 7986 in 3 years find sum of rate percent

Answer 1

$\huge \underline \mathfrak\red{Question}$

A certain sum of money at compound interest amount rupees 6600 in years and 7986 in 3 years find sum of rate percent

$\huge \underline \mathfrak\green{Answer}$

Amount in one year = 6600 /-

$\implies \rm{P[1+ \frac{r}{100} ]= 6600}.....i$

Amount in 3 years = 7986 /-

$\implies \rm{P [{1+ \frac{r}{100} }]^{3} }=7986......ii$

on dividing ii by i , we get :

$\rm{ \dfrac{P[1+ \dfrac{r}{100}]^3 }{P[1+ \dfrac{r}{100} ]^1} }= \dfrac{7986}{6600} \implies [ 1+ \dfrac{r}{100}] ^2= \dfrac{121}{100}$

$\implies \rm{ \: 1 + \dfrac{r}{100} } = \dfrac{11}{10}$

$\boxed { \implies \rm{rate= 10 percent }}$

$\rm{now} \:P[1+ \dfrac{r}{100} ]^1 = 6600 \implies \: P[1+ \dfrac{10}{100} ]^1=6600$

$\boxed { \red{\implies \rm{\: P = 6000 /-}}}$

$\boxed{ \red {\implies \rm{ \: r\: = 10 \: percent}}}$

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$\rm \underline \red{</strong><strong>FORMULA</strong><strong>S</strong><strong> \: </strong><strong>ARE</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> AS \: FOLLOWES :-}$

$</strong><strong>\</strong><strong>i</strong><strong>m</strong><strong>p</strong><strong>l</strong><strong>i</strong><strong>e</strong><strong>s</strong><strong> </strong><strong>\rm{ \: A = P [ 1 + \dfrac{r}{100}]^n }$

where A is amount

P is principal

and r is rate of interest

and n is number of years

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