Question

Approximately how long will it take for $700 to double if it is invested at 4% annual

Answer 1

Answer: 17 years

Step-by-step explanation:

Exponential equation for compund amount( compunded continuously):

$A=Pe^{rt}$ , where P= Principal value , r= rate of interest , t= time.

Given: A= 2P

r =4%= 0.04

To find : t

Substitute all values in the formula , we get

$2P=Pe^{0.04t}\\\\\Rightarrow\ 2=e^{0.04t}$

Taking natural log on both sides

$\ln2=\ln e^{0.04t }\\\\\Rightarrow\ 0.693147=0.04t\\\\\Rightarrow\ t=\dfrac{ 0.693147}{0.04}\\\\\Rightarrow\ t=17.3286\approx17$

hence, it will take 17 years (approx).