A) 12 yr
B) 13 yr
C) 8 yr
D) 16 yr
Correct Answer: C
$ \Rightarrow $ $ \frac{A}{P}={{( 1+\frac{r}{100} )}^{4}} $
$ \Rightarrow $ $ 2={{( 1+\frac{r}{100} )}^{4}} $ On squaring both sides, we get $ 2^{2}={{( 1+\frac{r}{100} )}^{8}} $
$ \Rightarrow $ $ 4={{( 1+\frac{r}{100} )}^{8}} $
$ \therefore $ It will become 4 times itself in 8 yr. Alternate Method If a certain sum, at compound interest becomes x time in $ t _1yr $ and $ y $ times in $ t _2yr. $ Then, $ {x^{\frac{1}{t _1}}}={y^{\frac{1}{t _2}}} $ Given, $ t _1=4yr, $ $ x=2, $ $ t _2=? $ and $ y=4 $
$ \Rightarrow $ $ {{(2)}^{1/4}}={{(4)}^{1/t _2}} $
$ \Rightarrow $ $ {{(2)}^{1/4}}={{(2)}^{2/t _2}} $ On comparing both sides, we get $ \frac{2}{t _2}=\frac{1}{4} $
$ \therefore $ $ t _2=8yr $