A married couple is trying to finance their three$-$year$-$old son$$s college education. Money can be deposited at the end of each quarter at $8\%$ interest compounded quarterly.

a$)$ What end$-$of$-$quarter deposit must be made from the son$$s $3$rd birthday to his $18$th birthday $(15$ years$)$ to provide $$80,000$ on each birthday from the $19$th to the $22$nd $(4$ years$)?$

b$)$ Draw the cash flow in the white space below.