Question 624014
How many years will it take $6,000 to amount to $8,000 if it is invested at an annual rate of 9.0% compounded continuously?
<pre>
A = Pe<sup>rt</sup>

A = final amount = 8000
P = beginning amount = 6000
r = rate expressed as a decimal = .09
t = the number of years = (unknown)

8000 = (6000)e<sup>(.09)t</sup>

Divide both sides by 6000

{{{8000/6000}}} = e<sup>.09t</sup>

{{{4/3}}} = e<sup>.09t</sup>

Since A = e<sup>B</sup> is equivalent to B = ln(A),

,09t = ln({{{4/3}}})

   t = ({{{4/3}}})÷.09

   t = 14.81481481...

Answer: about 15 years.

Edwon</pre>