Though economists may wish differently, humans are far from rational. This is the biggest reason why so many people contribute to savings accounts while they still have debt.
The most important thing to understand is that there are very few savings accounts which offer comparable interest to credit cards. Take this example: if you have $10,000 in a savings account earning 5% per year and $5,000 on a credit card at an interest rate of 20% per year, your net worth after five years is zero.
While your savings will grow by $2,500, your debt has grown by $7,500, due to the difference in interest rates. This leads to the fact that it's always better to pay off debt if the interest rate on it is higher. Though you may want to keep the savings so that you can keep your pride, realize that will cost you in real money.
Saving Just ‘Feels Better
There's no denying that it feels better to save. Saving feels like building a foundation for your future, which is a far cry from simply paying off debt. You may envision any savings you have as for the kids education, or for improving your house, or whatever else – and it's in an account earning a good rate of interest. However, this strategy will only cost you if you've got high-interest debt.
Be Financially Healthy
As stated earlier, having money to pay off debt and keeping the debt is highly irrational. Debt is for people who don't have the money, and need to borrow it. If for example you keep your savings in the same bank where you have a credit card, then you are in effect paying for the privilege of borrowing your own money from them. This can only hurt you.
There are more positive reasons for paying debt which aren't only related to the difference in interest. First, you'll be less stressed about your debts. Second, your credit report will be better because you were able to pay everything back. This has the added effect of getting you a much better interest rate if you ever need to go into debt again.
While all of this can be difficult to stomach, it really is wiser to pay off debt first. Though you may get the feeling that you're spending away your savings and thus your future, understand that the debt you have means you already did that. So, do the next smart move and reduce your debt, even if it takes away most or all of your savings.