Question 1153394

Use the formula {{{A=P(1+r/n)^rt}}}

{{{r=16​}}}%={{{0.16}}}
{{{n=12}}}-compounded monthly

you want {{{A = 2P}}}  (double your money)

{{{2P=P(1+0.16/12)^(0.16t)}}}

{{{2=(1+0.13333)^(0.16t)}}}

{{{2=(1.13333)^(0.16t)}}}.......use log

{{{log(2)=log((1.13333)^(0.16t))}}}

{{{log(2)=(0.16t)log(1.13333)}}}

{{{log(2)/(0.16*log(1.13333))=t}}}

{{{t=log(2)/(0.16*log(1.13333)) }}}

{{{t=log(2)/log(1.13333^0.16)}}}

{{{t=34.6}}}  years


Compounded​ continuously:

{{{A=P*e^(rt)}}}

you want {{{A = 2P}}}, and {{{r=16​}}}%={{{0.16}}}

{{{2P=P*e^(0.16t)}}}

{{{2=e^(0.16t)}}}.....use natural log

{{{ln(2)=ln(e^(0.16t))}}}

{{{ln(2)=(0.16t) ln(e)}}}

{{{ln(2)=(0.16t) *1}}}

{{{0.16t=ln(2)}}}

{{{t=ln(2)/0.16}}}

{{{t=4.33217}}} years