Example $1$

A person will now deposit geometrically incremental cash into his daughter's account every six months so that she can withdraw $800$$ every three months from her bank account during her university years. The first payment to the account will be made when her daughter, now $8$ years old, turns $10.$ The geometric increase rate will be $2\%$ every six months and the final payment will be made when the daughter turns $14.$ The first cash withdrawal from the account will be made when the girl turns $18,$ and the last withdrawal will be at the end of her $21$st birthday. What should the first payment be made by the father? The time value of money is $12\%$ compounded quarterly.