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6.Interest
hard
If in a certain number of years, ₹ $3000$ amounts to ₹ $4320$ at a compound interest, in half that time ₹ $3000$ will amount to (In ₹)
A
$3400$
B
$3600$
C
$3800$
D
$3520$
Solution
(b) Let, $r \%$ be the rate and $n$ years be the time.
Then, $4320=3000\left(1+\frac{r}{100}\right)^{n}$
$\therefore \quad\left(1+\frac{r}{100}\right)^{n}=\frac{4320}{3000}=1.44$
$\therefore \quad\left(1+\frac{r}{100}\right)^{n / 2}=\sqrt{1.44}=1.2$
$\therefore \operatorname{In} \frac{n}{2}$ years, ₹3000 will amount to
$3000\left(1+\frac{r}{100}\right)^{n / 2}=3000 \times 1.2$
$=₹ 3600$
Standard 13
Quantitative Aptitude
