A finance company declares that, at a certain compound interest rate, a sum of money deposited by anyone will become 8 times in 3 years. If the same amount is deposited at the same compound rate of interest, then in how many years will it become 16 times?
(a)4 years
(b)5 years
(c)6 years
(d)7 years
Answer
Answer (as printed): A
Explanation
$P\left(1+\frac{R}{100}\right)^{3}=8 P \Rightarrow\left(1+\frac{R}{100}\right)^{3}=8$. Let $P\left(1+\frac{R}{100}\right)^{n}=16 P \Rightarrow\left(1+\frac{R}{100}\right)^{n}=16=2^{4}=\left(2^{3}\right)^{4 / 3}$ $$\begin{aligned} & \Rightarrow\left(1+\frac{R}{100}\right)^{n}=(8)^{4 / 3}=\left\{\left(1+\frac{R}{100}\right)^{3}\right\}^{4 / 3}=\left(1+\frac{R}{100}\right)^{4} . \\ & \Rightarrow n=4 . \end{aligned}$$ ∴ Required time $=4$ years.
Explanation as extracted from the printed page; notation may be imperfect.