a) 45 years
b) 48 years
c) 54 years
d) 60 years
Answer: a
Explanation:
$$\eqalign{
& P{\left( {1 + \frac{{\text{R}}}{{100}}} \right)^{15}} = 2P \cr
& \Rightarrow {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^{15}} = 2 \cr
& {\text{Let }}P{\left( {1 + \frac{{\text{R}}}{{100}}} \right)^n} = 8P \cr
& \Rightarrow {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^n} = 8 = {2^3} = {\left\{ {{{\left( {1 + \frac{{\text{R}}}{{100}}} \right)}^{15}}} \right\}^3} \cr
& \Rightarrow {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^n} = {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^{45}} \cr
& \Rightarrow n = 45 \cr} $$
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