posed as it is, the question can be interpreted in several ways:
- 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?
- 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):
LI(x) = Lifetime Income
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)...