Question 121739
Remember the formula for compounding interest continuously is



{{{A=Pe^(rt)}}} where A is the return, P is the principal, r is the interest rate and t is the time



So if we want to know when our money will double, this means that A will be twice as much as P. In other words, {{{A=2P}}}



{{{A=Pe^(rt)}}} Start with the given formula



{{{2P=Pe^(0.05t)}}} Plug in {{{A=2P}}} and {{{r=0.05}}} note: 5% is the decimal number 0.05



{{{2P/P=e^(0.05t)}}} Divide both sides by P



{{{2=e^(0.05t)}}} Divide



{{{ln(2)=0.05t}}} Take the natural log of both sides. This will eliminate the base "e"




{{{ln(2)/0.05=t}}} Divide both sides by 0.05 to isolate t




{{{0.69315/0.05=t}}} Use a calculator to evaluate {{{ln(2)}}}. Note: {{{ln(2)=0.69315}}}



{{{13.863=t}}} Divide 




Now if you round to the nearest hundredth, the answer is:



{{{t=13.9}}}


So it will take about 13.9 years to double any given sum of money



So the answer is B)