Question

At what rate percent will a sum of money double itself in $6$ years ?

Answer 1

Let principal $=\mathrm{P}$

Rate of interest $=\mathrm{R}\%$

Given: Amount $=2\mathrm{P}$

Since, Amount $=$ Principal $+$ Simple Interest

$$\begin{gathered} \Rightarrow 2\mathrm{P}=\mathrm{P}+\mathrm{S}.\mathrm{I}. \\ \Rightarrow \mathrm{S}.\mathrm{I}.=2\mathrm{P}-\mathrm{P} \\ \Rightarrow \mathrm{S}.\mathrm{I}.=\mathrm{P} \end{gathered}$$

We know that

Simple interest $=\frac{\mathrm{P}\times \mathrm{R}\times \mathrm{T}}{100}$

Then,

$\mathrm{P}=\frac{\mathrm{P}\times \mathrm{R}\times 6}{100}$
$$\begin{gathered} \Rightarrow \mathrm{R}=\frac{100\times \mathrm{P}}{6\times \mathrm{P}} \\ \Rightarrow \mathrm{R}=\frac{100}{6} \\ \Rightarrow \mathrm{R}=16.66\% \end{gathered}$$

Hence, the required interest rate is $16.66\%$.