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Student loan payments and opportunity costs
If I understand correctly, your question boils down to this: "I have $X to invest over 25 years, are guaranteed returns at a 0.6% lower rate better than what I expect to get from the stock market over the same period?" Well, I believe the standard advice would go something like: Rational investors pay a premium to reduce risk/volatility. Or, put another way, guaranteed returns are more valuable than risky returns, all things equal. I don't know enough about student loans in America (I'm Australian). Here a student loan is very low interest and the minimum repayments scale with what you earn not what you owe, starting at $0 for a totally liveable wage - Here I'd say there's a case to just pay the minimum and invest extra money elsewhere. If yours is a private loan though, following the same rules as other loans, remember the organisation extending your loan has access to the stock market too! why would they extend a loan to you on worse terms than they would get by simply dumping money into an index fund? Is the organisation that extends student loans a charity or subsidised in some way? If not, someone has already built a business on the the analysis that returns at 6.4% (including defaults) beats the stock market at 7% in some way. What I would put back to you though, is that your question oversimplifies what is likely your more complex reality, and so answering your question directly doesn't help that much to make a persuasive case - It's too mathematical and sterile. Here are some things off the top of my head that your real personal circumstances might convince you to pay off your loan first, hit up Wall Street second: