# How long does it take for a college educated person to catch up in salary to a non-college educated person?

case questions quant problems
Recent activity on Oct 08, 2018
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Was asked this question in a case and it stumped me for some reason.

College costs 30k a year, starting salary is 60k, in 10 years it is 100k.

Non-college salary starts at 40k, in 10 years it is 75k.

What I was supposed to look for was the point at which the college educated person caught up with the non-college educated person with no debt. Any help is greatly appreciated--this is likely a lot simpler than I am making it out to be!

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Hi Anonymous,

posed as it is, the question can be interpreted in several ways:

1. If one person starts to work now, while the other one attends college, when do their lifetime incomes meet if a) you exclude the cost of college or b) you include the cost of college?
2. If one person starts to work now, while the other one attends college, when do their annual incomes meet?

I assume that it's No. 1b (makes most sense). The tricky part comes from rising annal salaries. Also, it's not entirely well defined what "in 10 years" means. After 10 years of working (what I am assuming) or in 10 years from today. But in the end it's relatively straightforward. Mathematically it would be a couple of integrals that need to be solved for time.

They should look something like this (assuming 4 years of college):

t = Time

LI(c) = (-30 * 4) + 60 * (t-4) + 4 * (t-4) | for all t > 4

LI(nc) = 40 * t + 3.5 * t

LI(c) = LI (nc)

You'd be surprised how long it takes (assuming that income growth will remain the same)...

(edited)