Question $2$:

Your parents have accumulated a $$125,000$ nest egg. They have been planning to use this money to pay college costs to be incurred by you and your sister, Sarah. However, Sarah has decided to forgo college and start a business. Your parents are giving Sarah $$20,000$ to help her get started, and they have decided to take year$-$end vacations costing $$10,000$ per year for the next four years.

How much money will your parents have at the end of four years to help you with graduate school, which you will start then? You plan to work on a master's and perhaps a PhD$.$ If graduate school costs $$26,353$ per year, approximately how long will you be able to stay in school based on these funds? Use $9$ percent as the appropriate interest rate throughout this problem.