One simple way you might think about it: If you loan me $25k at 0% interest, I will take it and invest it in my portfolio for an estimated 7% return. I will make $1750/year off that money. And I would prefer to keep that loan for as long as possible, to keep raking in that return. Yes, you'd certainly be leaving money on the table by paying the loan off.
Procrastinating at work, I threw some numbers into an Excel sheet. For simplicity's sake, let's say you actually had $25k in cash today and could pay off the loan immediately. That would earn you a $0 investment return. If instead you paid the minimum, at a 7% annual return (0.57% monthly return), you'd be expected to earn $3729 over the course of the 53 months it would take you to pay off the loan. Or if you're including the compounding from the original returns, it's more like $4555.
Your scenario will be less than that, since you're not making an immediate investment of $25k. But if you start socking away $1900 each month, and you invest a big lump sum of $13k in September, you'll still be making several thousand dollars of return over the next few years.
The other thing that people don't account for in these calculations is taxes.
A few caveats:
- We don't know what the market will do, blah blah blah. One advantage of paying off debt is that there's zero risk.
- There is a certain psychological value in getting rid of debt (especially if it's important to your wife), even if it's not the smartest move, strictly by the numbers.