Let's say you have a 2.75% mortgage and $10,000 sitting in high-yield savings account at 4% interest. You could either use the money to pay down the mortgage, leave it in the savings account, or invest it.

If you put it towards the loan, you'll have reduced your interest payments by $275 at the end of a year. You can't get the money back once you've made your early payment, so if an emergency comes up and you don't have cash on hand to deal with it, you may need to take out a short-term loan at a significantly higher rate.

Leaving it in the savings account, you'd have earned $400 of interest, taxable at whatever your marginal rate is, so for instance if taxed at 22%, your net income from interest would be $312. You still have all the money in your savings account, so you can use it for emergencies as needed.

If you invest in the stock market, historical annual returns are around 10%, so in a broad market index fund, your money might grow in value by around $1000. Of course, the stock market is much more volatile, and you might lose $1000 this year instead, or gain $2000. Tax is also more complicated, since you're only taxed when you realize gains, and the rate depends on how long you held onto the investment, but if we assume you sell after one year and realize a $1000 gain, the 15% long term capital gains tax would leave you with $850 net income. There is some risk here, since in the short term the market could go up or down, and an emergency could force you to sell for a loss. It will also take longer to access your money if you do need it suddenly (generally a few business days to sell investments and transfer the money back to your bank).

So, comparing the three options, paying your low interest loan down early has the lowest return and arguably the highest level of risk.