Question 381160
<br><font face="Tahoma">When compounding continuously, we use the formula: <br>

{{{A=P*e^(r*t)}}}<br>

Where A is the accumulated value, P is the principal, r is the rate, and t is the time in years.<br>

So we are given A=11300 r=.055 P=5000<br>

{{{11300=5000*e^(.055*t)}}}<br>

{{{11300/5000=e^(.055*t)}}}<br>

{{{2.26=e^(.055*t)}}}<br>

{{{ln(2.26)=ln(e^(.055*t))}}}<br>

{{{ln(2.26)=.055*t*ln(e)}}}<br>

{{{ln(2.26)=.055*t*1}}}<br>

{{{ln(2.26)/.055=t}}}<br>

{{{t=14.82481479}}}<br>

So it would take right around 14.825 years for the original $5000 to grow to $11300.<br>

I hope this helps!<br>