Question 920671
A, amount; p, principal, t, how many time compounding periods to reach A.


{{{highlight_green(A=p(1+0.03/4)^(t))}}};  this is what you are trying to express.
Note that the quarterly interest rate is one fourth of the yearly rate, and the
number of compounding periods is {{{t}}}.


Sovle for t, and then substitute A=200 and p=150.


Some of the algebraic steps:
{{{A=p(1.0075)^(t)}}}
{{{1.0075^(t)=A/p}}}
You can choose any logarithm base desired.
{{{log(((1.0075)^(t)))=log((A/p))}}}
{{{t*log((1.0075))=log((A/p))}}}
{{{t=(log((A/p))/log((1.0075)))}}}
{{{highlight(t=log((A/p))/(log((1.0075))))}}}


TIME PERIODS:  {{{highlight(t=38.5)}}}
which is 9.625 years, but in strict amount of quarter periods of the year, {{{highlight(9&3/4)}}} years.