Let's put it another way. Suppose you have a $100,000 mortgage on which you're paying 6% interest. You have a savings account with $2,000 in it that pays 2% interest.
The savings account is costing you 4% per year.
Faced with this, one is better off putting extra cash into paying down the mortgage rather than in a savings account. It puts one in a "cash poor" position, which is not the same as being poor.
> Faced with this, one is better off putting extra cash into paying down the mortgage rather than in a savings account.
Cash poor means no easily accessible source of cash, it doesn't refer to the amount of money in your wallet. In your scenario you can access that cash again by jumping onto the banks website (or even visiting the bank) and moving it to your everyday account.
I used the term cash poor correctly for the scenario where you used your savings account to buy down the mortgage a bit. It's not quite so easy to increase the mortgage amount, it would depend on what the terms are if you are late or underpay a mortgage payment. If the terms are good, it is one way to recover the cash for an emergency.
It seems logical to pay off debts as soon as you can as they're expensive. However, in your example, if I use that $2,000 to pay down (a tiny bit of) my mortgage, I put myself in a dangerous position by not being able to come up with some extra cash in case of emergency. I hope most people with mortgages wouldn't do that.
It all depends on one's risk tolerances are and what other options for obtaining money there are (like being late or underpaying the next mortgage payment).
Keep in mind that taking on a mortgage itself is a risky move, as people found out in 2008.
BTW, even paying a few dollars extra a month on a 30 year mortgage can be surprisingly effective, since nearly all the early payments are interest, not principal.
The savings account is costing you 4% per year.
Faced with this, one is better off putting extra cash into paying down the mortgage rather than in a savings account. It puts one in a "cash poor" position, which is not the same as being poor.