# The Present Value of Learning, Adjusted for Forgetting

Suppose learning marginal fact F increases your productivity by V. What is the present value of learning F? Economists will be tempted to mechanically apply the standard present value formula. Using discrete time to keep things simple:

PDV(F)=V + V/(1+r) + V/(1+r)^2 + V/(1+r)^3 + … = V/r.

If V=$100, and r=5%, the present value of learning F is $2000.

As Treebeard would say, however, “Don’t be hasty.” When you learn F, this hardly implies that you will know F forever. Every observant teacher knows that the opposite is closer to the truth: students usually quickly forget what they learn.

How quickly? A large literature on summer learning loss finds that students lose roughly one month of learning for every three months they spend out of school. As a major meta-analysis explains:

The meta-analysis indicated that the summer loss equaled about one month

on a grade-level equivalent scale, or one tenth of a standard deviation relative to spring test scores.

This result probably doesn’t hold along the entire range of learning. As a previous post documented, students who master a subject by overlearning have excellent retention. But the summer learning loss estimate seems fully applicable to *marginal* facts. So let’s apply it:

PDV(F)=V + .66V/(1+r) + .33V/(1+r)^2

[Note the absence of ellipses at the end of the equation!]

If V=$100, and r=5%, the present value of learning F is just $192.79. The present value of learning adjusted for forgetting is over 90% less than the present value without forgetting.

And that is why economists must never forget to adjust for forgetting! *Arrested Development* allusion intentional.