Question 954649
2%, same as 0.02, if compounded quarterly means each period of compounding the rate is {{{0.02(1/4)=0.005}}}


{{{200=100*(1.005)^p}}}, using p to count the periods.


One way to solve is to find p, and then find {{{p/4}}} to find how many years.
Other way is  p/4=y for years, {{{p=4*y}}}  and do the equation as
{{{200=100*(1.05)^(4y)}}}.


{{{(1.005)^p=2}}}
{{{log(10,1.005)*p=log(10,2)}}}
{{{p=log(10,2)/log(10,1.005)}}}


{{{p=140}}}----quarters
{{{y=140/4=highlight(34&3/4)}}}----years