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A sum of money placed at compound interest doubles itself in 4 years. In how many years will it amount to 8 times?
Options:
A .  10 years
B .  8 years
C .  6 years
D .  12 years
Answer: Option D

Answer : Option D

Explanation :

Let the sum be Rs.1 which becomes Rs.2 after 4 years
$MF#%\Rightarrow 2 = 1\left(1 + \dfrac{\text{R}}{100}\right)^4 \quad \color{#F00}{\text{--- (equation 1)}}$MF#%
Let the sum of Rs.1 becomes Rs.8 after n years
$MF#%\Rightarrow 8 = 1\left(1 + \dfrac{\text{R}}{100}\right)^n \quad \color{#F00}{\text{--- (equation 2)}}\\\\ \Rightarrow (2)^3 = 1\left(1 + \dfrac{\text{R}}{100}\right)^n \\\\ \Rightarrow \left[1\left(1 + \dfrac{\text{R}}{100}\right)^4
\right]^3 = 1\left(1 + \dfrac{\text{R}}{100}\right)^n \quad \color{#F00}{\text{(∵ replaced 2 with the value in equation 1)}}\\\\ \left(1 + \dfrac{\text{R}}{100}\right)^{12} = \left(1 + \dfrac{\text{R}}{100}\right)^n\\\\ \text{n} = 12$MF#%
i.e., the sum amounts to 8 times in 12 years



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