A sum of money placed at compound interest doubles itself in 5 ,years . It will amount to eight time

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6.Interest

hard

A sum of money placed at compound interest doubles itself in $5 \,years$. It will amount to eight times itself at the same rate of interest in (In $years$)

$7$

$10$

$15$

$20$

Solution

$2 P=P\left(1+\frac{R}{100}\right)^{5}$

Let the number of years at which amount becomes 8 times be $N$.

$\therefore \quad 8 P=P\left(1+\frac{R}{100}\right)^{N}$

$(1) \Rightarrow \quad\left(1+\frac{R}{100}\right)^{5}=2$

$\frac{(2)}{(1)} \Rightarrow \frac{8 P}{2 P}=\frac{P\left(1+\frac{R}{100}\right)^{N}}{P\left(1+\frac{R}{100}\right)^{5}}$

on substitution from $(3),$ we get,

$4=\frac{\left(1+\frac{R}{100}\right)^{N}}{2}$

Or $\left(1+\frac{R}{100}\right)^{N}=8$

(3) $\Rightarrow \quad\left(1+\frac{R}{100}\right)^{5}=2$

$\therefore \quad(4) \Rightarrow \quad\left(1+\frac{R}{100}\right)^{N}=2^{3}=\left[\left(1+\frac{R}{100}\right)^{5}\right]^{3}=\left(1+\frac{R}{100}\right)^{15}$

$\therefore \quad N=15$ years

Standard 13

Quantitative Aptitude

If the compound interest on a certain sum for $2$ years is ₹ $60.60$ and the simple interest is ₹ $60$, then the rate of interest per annum (In $\%$) is

easy

Abhinav invested a certain amount at the rate of $8$ $p.c.p.a.$ for $5$ years and obtained a $SI$ of $Rs. 3800.$ Had he invested the same amount at the same interest for $2$ years, how much amount (In $Rs.$) would she have obtained as $CI$ at the end of $2$ years?

medium

The compound interest on $\$ 1,800$ at $10 \%$ per annum for a certain period of time is $\$ 378 .$ Find the time in years.