Question

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a) Suppose the annual interest rate is 10%. Would you prefer obtaining 1000 $ today or 1150 $ in a year from now?

b) Assume that you are 18 years old and deciding whether to go to college or start working.

If you work, you will earn a constant wage w_HS throughout your career. If you study, you pay tuition for four years and then earn a constant wage w_COL.

(i) Show the condition under which you choose to study.

(ii) Explain how changes in tuition, in the interest rate and in the wage differential (w_COL – w_HS) would affect your decision.

Answer 1

1.

A

If annual interest rate = 10%

Then,

Future value of $1000 in 1 year = 1000*(1+10%) = $1100

So, it is good to get the $1150 after one year, as it has higher value than the future value of today's $1000.

B.

1.

if present value of wage differential (W_COL – W_HS) is greater than the present value tuition and other related fees, then it is good to choose the study, as it will bring higher wages that will also cover the tuition fees paid.

2.

The increase in tuition fee, will require wage differential (W_COL – W_HS) to be greater as well to continue with the decision of study in college and vice versa. If tuition fee remains same, then increase in interest rate, will make present value of wage differential to be smaller. So, to continue with the study, wage differential should be greater.

If tuition fee remains same, then decrease in interest rate, will make present value of wage differential to be bigger. So, to continue with the study, wage differential can be smaller as well as long as its PV is greater than the PV of tuition fees.

If tuition fee and interest rate remain same, then increase in wage differential will strengthen the decision to study.  

If tuition fee and interest rate remain same, then decrease in wage differential will weaken the decision to study and it can make PV of wage differential to be less than the PV of the tuition fee. So, student can also opt for the work.