If Rs. 3000 amounts to Rs. 4320 at compound interest in a certain time, then Rs. 3000 amount to what

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6.Interest

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If $Rs. 3000$ amounts to $Rs. 4320$ at compound interest in a certain time, then $Rs. 3000$ amount to what in half of the time (In $Rs.$) ?

A

$3400$

B

$3600$

C

$3800$

D

$3520$

Solution

Let rate $= R \%$ and time $= n$ year

Then, $4320=3000\left(1+\frac{ R }{100}\right)^{ n }$

$\Rightarrow\left(1+\frac{ R }{100}\right)^{ n }=\frac{4320}{3000}=1.44$

$\therefore \quad\left(1+\frac{ R }{100}\right)^{\frac{\pi / 2}{2}}=\sqrt{1.44}=1.2$

$\therefore$ Required amount for $\frac{ n }{2}$ year

$=3000\left(1+\frac{ R }{100}\right)^{\frac{\pi / 2}{2}}=3000 \times 1.2= Rs .3600$

Standard 13

Quantitative Aptitude

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