You are considering whether or not to go to graduate school. Well... there are many things to consider, of course, such as the type of job you would thus get, the opportunity to live in a city or town whose existence you might have disregarded entirely otherwise and, most importantly, the sheer and ecstatic joy of learning! (By now, you may be wondering what I am on and where you can get some - search no further than Durian, a pungent fruit available in Chinatowns across NYC). All right, all this is well and good, but there is also a monetary aspect... Financially, would it be a sound decision? Let's see.

For the purposes of this exercise, we will assume there is no inflation.

-   The graduate program you are looking at lasts four years;

-   The school forbids you to work during the time of the program (to leave all your time to studying), but they will give you 10 000$ a year to live on

-    The programwill allow you to get a job paying 70 000 a year when you get out.

-   If you do not go to graduate school (assuming you are just graduating from college), you have a job lined up paying45 000.

-    Your discount rate is 10% (0.1).

a)  Is this a good idea financially? That is, does the higher wage when you get out ever compensates for the lower income during grad school? If so, how many years must you work on the job after graduation in order to come up ahead? (don't forget to discount the future!)

b)  What if you have another option: A school that lends you the money, but promises a job at 90 000$ when you get out. Let's say that the school lends you the 10 000$ a year instead, and that repayment is due whenever you want (say, within 20 years), but as soon as you graduate, the loan starts accruing interest at a rate of 10% a year (so you owe 40 000$ on the day of graduation, 44 000$ the next year if you don't pay anything, etc.). In this case, how many years do you need at 90 000$ for you to come out ahead? If you do come start coming out ahead after a while, do you do so faster than at the free school?

c)   We talked to some extent about the issue of debt peonage in class. Even if you come out ahead eventually with the deal in b), is it constraining in away in terms of life plans? If so how?

d)   So far, I have assumed that you have all the information (job-wise, etc.) in advance and that you know the information for certain. Of course, life is not so simple and no job is ever entirely guaranteed... So in this case, on what would you base your decision (keeping it on financial considerations for now)? How solid of a basis do you feel this is? Does taking uncertainty into account change the assessment of whether you should take a loan to study or not? If so, how does it change it?

Please outline all your calculations and your reasoning. Points will be given both for the reasoning and the end answer.