I am having a hard time trying to figure out how to begin analyzing the compounding quarterly can anyone suggest anything?

Are you referring to interest, and what do you mean by "analyzing" it? What exactly are you trying to do here?

well, basically compounding quarterly is about compounding the total inflow or outflow for three months (a quarter) than calculate it with the related factors. I'll give u an example for compounding interest:
Mr.A stores $100 monthly to his bank account and the bank annual interest rate is 8%, compounded quarterly.
Since its quarterly compounded, then we have to calculate effective interest rate using the formula below:
I effective =(1+(r/m)^m)-1; where r=nominal interest & m=number of compounding periods.
in this example:
r = 8% & m=4 (quarterly =3months --> 12/3=4)
so the effective rate will be = 8.24% annually
then the amount of interest expense received by mr.A in one year is = 8.24%*(12*100)= $99