$\begin{array}{1 1} 1648 \\ 1500 \\ 1300 \\ 1200\end{array} $

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- $\large\frac{dp}{dt} =\frac{ r}{100}$$.p$ where $p,r,t$ are principal,rate and time respectively

Step 1:

Given: Principal increases continuously at the rate of 5% per year

Hence $\large\frac{dp}{dt}=(\large\frac{5}{100})$$p$

$\large\frac{dp}{dt} =\frac{ p}{20}$

Now seperating the variables we get

$\large\frac{dp}{p}=\frac{dt}{20}$

Step 2:

Integrating on both sides we get

$\int\large\frac{dp}{p}=\frac{1}{20} $$\int dt$

$\log p = \large\frac{t}{20 }$$+C$

Hence $p=e^{(\Large\frac{t}{20}+C)}$

Step 3:

When $t=0, p=1000$

Hence $1000= e^C$

When $t=10$ , $p=e^{\Large(\frac{1}{2}+C)}$

or $p=e^{(0.5)}.e^C$

$p=1.648 (1000)$ [given $e^{0.5}=1.648]$

Therefore after 10 years the amount is worth Rs1648

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