Question 190889
If $500 is invested at 7% compounded continuously, how long would it take for the value of the investment to reach $800?
<pre><font size = 4 color = "indigo"><b>
The equation for continuous compounding is

{{{A = Pe^(rt)}}}

where 

P = the Principal, which is the same as the starting amount = $500
A = the AFTER amount, which is the same as the ending amount = $800
r = the rate expressed as a decimal, 0.07
t = the number of years it takes for the Principal to become the 
    AFTER amount.  That's the unknown that we want to find.
e = 2.718281828459
So we substitute everything but t in

{{{A = Pe^(rt)}}}

{{{800 = 500e^(.07t)}}}

Divide both sides by 500

{{{1.6 = e^(.07t)}}}

Use this rule: 
The exponential equation{{{A = e^B}}} is equivalent to {{{B=ln(A)}}}

{{{.07t=ln(1.6)}}}

Divide both sides by .07:

{{{t = ln(1.6)/.07}}}

{{{t = 6.714337561}}}

About 6.7 years.

Edwin</pre>