Question

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

interest, compounded continuously?
Round your final answer to the nearest whole year and do not label units.

Answer 1

Answer: 17 years

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=( 0.693147)/(0.04)\\\\\Rightarrow\ t=17.3286\approx17`

hence, it will take 17 years (approx).