aladner comments on Harry Potter and the Methods of Rationality discussion thread, part 14, chapter 82 - Less Wrong
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I'm surprised that people think saving Hermione for ~$3.4MM was expensive. It does mean Harry needs money soon, but if her intelligence plus magic gets her a VP position at an investment bank, she can earn up to $.5MM per year (worked example: [1]). And Harry and Hermione could almost certainly come up with a better (ethical) plan.
Some presumably sophisticated real-world investors have actually invested in people in this way, e.g. investing $250K for a 2% stake in a "technologist's" income (worked example: [2]).
Again, Harry does need money soon-ish; but even if his magical hedge fund doesn't pan out, the-Boy-Who-Lived should be able to secure ten house-sized loans (abroad if necessary; Unbreakable Vows greatly reduce credit risk, and there must be people other than Draco who see the value of loaning money to HPJEV.)
(There are many possible objections, but both of these kids are really smart and have years to think about it. And magic.)
[1] Hermione takes five years to get to VP level, then saves an average of ~.5MM/year for fifteen years. After twenty years, she gives all of her savings to Harry and is freed from all further obligations. Harry has earned ~30% per year over this period, and Hermione has well over 150 years of life left. This may not be optimal, but it's clearly better for both than letting her rot in Azkaban.
[2] Multiply by 15 to get an investment of $3.8MM for a 30% stake. Harry pays less and ends up with whatever stake he likes - and unlike the investor, he can order Hermione to maximize her income. Hermione being a witch raises the value of the investment further.
It looks to me like they don't have quite enough time for Hermione to get a job as an investment banker. Of course, he still has plenty of options if the arbitrage trick doesn't work.
The present debate is not how he can fulfill his obligation. They are arguing specifically if Harry made a justified investment by paying such a high price to save Hermione's life. It seems conclusive that the pure monetary investment is actually sound, he can directly gain the money he invested back at a decent rate even besides the additional benefits of rescuing her.