* $\gamma_c > 1$ be the (gross) rate of growth of wages of a college graduate, so that

$ w_t^c = w_0^c \gamma_c^t$

* $D$ be the upfront monetary costs of going to college

If someone goes to work immediately after high school and works for the $T+1$ years $t=0, 1, 2, \ldots, T$, she earns present value

where

$$

A_c =w_0^c (R^{-1} \gamma_c)^4 \left[ \frac{1 - (R^{-1} \gamma_c)^{T-3} }{1 - R^{-1} \gamma_c } \right]

A_c = (R^{-1} \gamma_c)^4 \left[ \frac{1 - (R^{-1} \gamma_c)^{T-3} }{1 - R^{-1} \gamma_c } \right]

$$

The present value $c_0$ is the "human wealth" at the beginning of time $0$ of someone who chooses to attend college for four years and then start to work at time $t=4$ at the wage of a college graduate.