Question 190666
{{{A=P(1+r/n)^(nt)}}} Start with the compounding interest formula



{{{14000=7000(1+0.06/9)^(9t)}}} Plug in {{{A=14000}}} (this is double of 7000), {{{P=7000}}}, {{{r=0.06}}} and {{{n=9}}}



{{{2=(1+0.06/9)^(9t)}}} Divide both sides by 7000.



{{{2=(1+0.00667)^(9t)}}} Divide



{{{2=(1.00667)^(9t)}}} Combine like terms.



{{{log(10,(2))=log(10,((1.00667)^(9t)))}}} Take the log of both sides




{{{log(10,(2))=9t*log(10,(1.00667))}}} Rewrite the right side using the identity  {{{log(b,(x^y))=y*log(b,(x))}}}




{{{log(10,(2))/log(10,(1.00667))=9t}}} Divide both sides by {{{log(10,(1.00667))}}}.



{{{104.266=9t}}} Approximate the left side



{{{104.266/9=t}}} Divide both sides by 9.



{{{11.585=t}}} Divide



So the answer is approximately {{{t=11.585}}} which means that it takes about 11.585 years for $7,000 to double