Final answer:
After subtracting the initial $26,000 for Courtney and accounting for yearly vacations subtracted from compounded interest over four years, the remaining amount is calculated using the compound interest formula. This final figure is then divided by the annual graduate school cost to estimate the number of years the student can stay in school with these funds.
Step-by-step explanation:
To determine how much money the parents will have at the end of four years of graduate school, we need to account for the $26,000 given to Courtney, and the annual $12,000 vacations over the next four years, using a 6% interest rate.
Firstly, we subtract the $26,000 given to Courtney from the initial nest egg: $170,000 - $26,000 = $144,000. This amount will then accrue interest over four years. Using the compound interest formula, A = P(1+r/n)nt, where P is the principal amount ($144,000), r is the interest rate (0.06), n is the number of times the interest is compounded per year (assumed to be once), and t is the time in years (4), we can calculate the amount.
However, we must also subtract the yearly vacations costing $12,000 per year, which are taken at the end of each year and therefore do not accumulate interest within that year. The calculations of the compound interests and yearly deductions will lead to the final amount available at the end of four years.
For part (b), to find out how long the student can stay in graduate school with costs of $26,660 per year, we will use the remaining funds after the four years and yearly cost, dividing the available amount by the annual expense to estimate the number of years the funds will last.
The detailed steps involve further calculations to provide exact figures for parts (a) and (b) of the question. The answer for part (a) is approximately $144,000(1+0.06)4 - 4 * $12,000; whereas the duration of study in part (b) would be the total amount available divided by $26,660.