Question 218358


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



{{{50=40(1+0.04/365)^(365*t)}}} Plug in {{{A=50}}}, {{{P=40}}}, {{{r=0.04}}} (note: 0.04 is the decimal equivalent of 4%) and {{{n=365}}}



{{{50=40(1+0.0001096)^(365*t)}}} Divide {{{0.04/365}}} to get {{{0.0001096}}}.



{{{50=40(1.0001096)^(365*t)}}} Add.



{{{(50)/(40)=(1.0001096)^(365*t)}}} Divide both sides by {{{40}}}.



{{{1.25=(1.0001096)^(365*t)}}} Divide {{{50/40}}} to get {{{1.25}}}.



{{{log(10,(1.25))=log(10,((1.0001096)^(365*t)))}}} Divide {{{50/40}}} to get {{{1.25}}}.



{{{log(10,(1.25))=365*t*log(10,(1.0001096))}}} Pull down the exponent.



{{{log(10,(1.25))/log(10,(1.0001096))=365*t}}} Divide both sides by {{{log(10,(1.0001096))}}}.



{{{2036.0928773=365*t}}} Evaluate the left side with a calculator.



{{{2036.0928773/365=t}}} Divide both sides by {{{365}}} to isolate 't'.



{{{5.5783367=t}}} Divide.



{{{t=5.5783367}}} Rearrange the equation.



{{{t=5.58}}} Round to the nearest hundredth.



So it will take about 5.58 years for an initial investment of $40 to grow to $50 (compounded 365 times a year at 4%).