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6.Interest
medium
If a sum of money placed at compound interest, compounded annually, doubles itself in $5$ years, then the same amount of money will be $8$ times of itself in (In $years$)
A
$25$
B
$20$
C
$15$
D
$10$
Solution
(c) Let the principal be ₹1.
$\therefore \quad A=P\left(1+\frac{R}{100}\right)^{T}$
$\Rightarrow \quad 2=1\left(1+\frac{R}{100}\right)^{5}$
Cubing both sides,
$2^{3}=\left(1+\frac{R}{100}\right)^{5 \times 3}$
$\Rightarrow \quad 2^{3}=\left(1+\frac{R}{100}\right)^{15}$
$\therefore \quad$ Time $=15$ years
Standard 13
Quantitative Aptitude