Question 737848
Translate this into an equation.  Assign variables as understood or known or unknown before translating the description and question into the equation.


A=amount after some time
P=initial investment
r=the interest rate in decimal form

Semi-annual means twice per year.  To be simpler, each half a year is the time period, so let's use t=halfyear time period, and you want t to be 8.  Four years will have eight semiannual periods.


Your expected A will be 3*P, because you want the investment to be tripled after the 8 compounding semiannual periods.


{{{A=P(1+r)^t}}}
{{{3P=P(1+r)^t}}}
Simplify a little
{{{3=(1+r)^t}}}
Take logarithms of each side, for convenience I'm choosing natural logs,
{{{ln(3)=ln((1+r)^t)}}}
{{{ln(3)=t*ln(1+r)}}}
{{{ln(1+r)=(1/t)*ln(3)}}}
Put that into exponential form
{{{e^((1/t)*ln(3))=1+r}}}
Combining steps,
{{{highlight(r=-1+e^((1/t)*ln(3)))}}}


That is the answer in symbolic form, which you can now use to plug in your given values and find r in your example question.  You would use either an electronic calculator or maybe a simple computer program (or fancier software program if you have something of such.)


(The rendering is cutting off the top of some of the exponent symbols so I hope you can follow the steps in the process).