Your younger sister, Barbara, will start college in five years. She has just informed your parents that she wants to go to Eastern University, which will cost $$42,000$ per year for four years $($assumed to come at the end of each year$).$ Anticipating Barbara$$s ambitions, your parents started investing $$2,000$ per year five years ago and will continue to do so for five more years. Use $12$ percent as the appropriate interest rate throughout this problem.

Barbara is now $18$ years old $($five years have passed$),$ and she wants to get married instead of going to school. Your parents have accumulated the necessary funds for her education.

Instead of her schooling, your parents are paying $$22,000$ for her upcoming wedding and plan to take a year$-$end vacation costing $$15,000$ per year for the next Three years. Use Appendix A and Appendix D$.$

a$.$ How much will your parents have at the end of Three years to help you with graduate school, which you will start then? $($Round $"$PV Factor" to $3$ decimal places. Round the final answer to nearest whole dollar.$)$

Funds available $

b$.$ You plan to work on a master$$s and perhaps a Ph$.$D$.$ If graduate school costs $$57,800$ per year, approximately how long will you be able to stay in school based on these funds? $($Round the final answer to the nearest whole year.$)$

No$.$ of years