Question 1197286
<pre>
{{{A=P(1+r/n)^(nt)}}}

A = amount to become = 3205.09
P = principal = beginning amount = 2500
r = 5% = 0.05
n = 4 since compounding is quarterly, 4 times a year.

{{{3205.09=2500(1+0.05/4)^(4t)}}}

{{{3205.09=2500(1+0.0125)^(4t)}}}

{{{3205.09=2500(1.0125)^(4t)}}}

Divide both sides by 2500

{{{1.282036=1.0125^(4t)}}}

Take natural logs of both sides

{{{ln(1.282036)=ln(1.0125^(4t))}}}

Move the exponent 4t in front of the natural log

{{{ln(1.282036)=4t*ln(1.0125)}}}

Solve for t by dividing both sides by 4*ln(1.0125)

{{{ln(1.282036)/(4*ln(1.0125))=t}}}

{{{4.999980665=t}}}

Round to t=5 years

Edwin</pre>