Question 457955
Note: 900 doubles to 1800






{{{A=P(1+r/n)^(n*t)}}} Start with the compound interest formula



{{{1800=900(1+0.10/2)^(2*t)}}} Plug in {{{A=1800}}}, {{{P=900}}}, {{{r=0.10}}} (the decimal equivalent of 10%), and {{{n=2}}}.



{{{1800=900(1+0.05)^(2*t)}}} Evaluate {{{0.10/2}}} to get {{{0.05}}}



{{{1800=900(1.05)^(2*t)}}} Add {{{1}}} to {{{0.05}}} to get {{{1.05}}}



{{{1800/900=(1.05)^(2*t)}}} Divide both sides by {{{900}}}.



{{{2=(1.05)^(2*t)}}} Evaluate {{{1800/900}}} to get {{{2}}}.



{{{ln(2)=ln((1.05)^(2*t))}}} Take the natural log of both sides.



{{{ln(2)=2*t*ln(1.05)}}} Pull down the exponent using the identity  {{{log(b,(x^y))=y*log(b,(x))}}}.



{{{ln(2)/ln(1.05)=2*t}}} Divide both sides by {{{ln(1.05)}}}.



{{{0.693147180559945/ln(1.05)=2*t}}} Evaluate the natural log of {{{2}}} to get {{{0.693147180559945}}}.



{{{0.693147180559945/0.048790164169432=2*t}}} Evaluate the natural log of {{{1.05}}} to get {{{0.048790164169432}}}.



{{{14.2066990828905=2*t}}} Divide.



{{{14.2066990828905/2=t}}} Divide both sides by 2 to isolate "t".



{{{7.10334954144523=t}}} Divide.



{{{t=7.10334954144523}}} Rearrange the equation.



{{{t=7.1}}} Round to the nearest tenth (ie to the nearest tenth of a year).



Answer: 7.1 years.