Rebecca is $29$ and considering going to graduate school so she sits down to calculate whether it is worth the large sum of money. She knows that her first year tuition will be $$45,000,$ due at the beginning of the year $($that is$,$ right away$).$ She estimates that the $2$nd year of tuition would be $$47,000.$ She also estimates that her living expenses above and beyond tuition will be $$9,000$ per year $($assume this extra expense occurs at the end of each year only when she is in graduate school$)$ for the first year and will increase to $$10,000$ the next year. She expects to earn $$20,000$ for an internship $($Assume this inflow occurs one year from now$).$ Were she to forgo graduate school she would be able to make $$54,000$ at the end of this year and expects that to grow $3\%$ annually. With a graduate degree, she estimates that she will earn $$116,000$ per year after graduation, again with annual $3\%$ increases. Either way, she plans to work until $62.$ The interest$/$discount rate is $7\%.$ What is the NPV of her graduate education?