Question

The doubling time of an investment earring 6% interest if interest is compounded is ? Years

Answer 1

In general, the continuous compounding interest formula is

$\begin{gathered} P(t)=P_0e^{rt} \\ P_0\rightarrow\text{ initial amount} \\ r\rightarrow\text{ interest rate} \\ t\rightarrow\text{ time} \end{gathered}$

Therefore, in our case,

$\begin{gathered} P(t)=2P_0,r=6\%=0.06 \\ \Rightarrow2P_0=P_0e^{0.06t} \end{gathered}$

Solve for t as shown below

$\begin{gathered} \Rightarrow2=e^{0.06t} \\ \Rightarrow ln2=ln(e^{0.06t}) \\ \Rightarrow ln2=0.06tln(e)=0.06t \\ \Rightarrow t=\frac{ln2}{0.06} \\ \Rightarrow t\approx11.6 \end{gathered}$

Thus, the answer is 11.6 years.