Discussion
Ramesh gets double the amount in 9 years when invested at compound interest. In how many years will the amount become four times itself?
Answer: D
Compound growth is multiplicative, so doubling twice is the same as quadrupling.
\[ \left(1 + \frac{R}{100}\right)^{9} = 2 \]
\[ \left(1 + \frac{R}{100}\right)^{18} = \left[\left(1 + \frac{R}{100}\right)^{9}\right]^{2} = 2^{2} = 4 \]
So it takes 18 years. The rate never needs to be found.
This multiplicative behaviour is what separates compound from simple interest: under simple interest, doubling in 9 years means quadrupling in 27, since there the growth is additive.
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