Discussion

Explanation:

Amount due $=P{\left(1+\frac{r}{100}\right)}^t$

$$\begin{gathered} \Rightarrow 2P=P{\left(1+\frac{r}{100}\right)}^2 \\ \Rightarrow 2={\left(1+\frac{r}{100}\right)}^2 \end{gathered}$$

Now, the amount has to quadruple at same rate of interest.

$$\begin{gathered} \Rightarrow 8P=P{\left(1+\frac{r}{100}\right)}^t \\ \Rightarrow 8={\left(1+\frac{r}{100}\right)}^t \\ \Rightarrow 2^3={\left(1+\frac{r}{100}\right)}^t \\ \Rightarrow {\left[{\left(1+\frac{r}{100}\right)}^2\right]}^3={\left(1+\frac{r}{100}\right)}^t \\ \Rightarrow {\left(1+\frac{r}{100}\right)}^6={\left(1+\frac{r}{100}\right)}^t \end{gathered}$$

⇒ t = 6 years.

Alternately,

For CI, since amount doubles in 2 years, it means the amount will double every 2 years.

For the amount to become 8 (= 2³) times, it has to double 3 times. Hence, time required = 2 + 2 + 2 = 6 years.

Hence, option (c).

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