Question 1153391
Use the formula {{{A=P(1+r/n)^(nt)}}}

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

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

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

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

{{{2=(12.16/12)^(12t)}}}.......use natural log

{{{ln(2)=ln((12.16/12)^(12t))}}}

{{{ln(2)=(12t) ln(12.16/12)}}}

{{{12t=ln(2)/ ln(12.16/12)}}}

{{{t=ln(2)/ (12ln(12.16/12))}}}

{{{t}}}≈{{{4.36099}}}  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