First, pay off the cars.

Second, people instructing you to keep the mortgage and invest the difference, assume you can return greater than 2.875% but this might not happen.

• if you invest in stocks or other volatile asset class, it could simply perform poorly (U.S. stocks are fairly expensive. High price correlates strongly with lower returns)
• Even if the asset class does well your specific investing strategy might underperform. The Dalbar study shows mutual fund investors tend to underperform the S&P 500 consistently and by a large margin. In 2014 the average equity fund investor underperformed the S&P 500 by a massive 8.19%.
• Most people that have spare cash tend not to invest it fully, but spend it instead.

The point is future investment returns are not guaranteed, despite people speaking as if they are assured. Investing also takes a lot of work. It is surprising hard to do well.

Paying off your mortgage (in whole or in part) does guarantee you do not have to pay 2.875% interest. Not having a mortgage over your head has intangible value; the feeling of not being in debt a hundred thousand dollars is liberating and, for me, worth more than making some (likely small) investment return.

You are asking a question of how to allocate your assets and liabilities. The "proper" answer is you need to figure out what makes you and your wife comfortable.

• Do you want to attempt to get the highest return, while taking on the most risk?
• Do you want to take the most conservative path (paying off all debt)?
• Or something in between?

Figure out how much mortgage debt, cash, liquid investments makes you comfortable.