In the days when borrowing was cheap and savings account rates were healthy, the savvy investor knew the logical thing to do was to save or invest.
In the current climate with saving accounts offering such poor return on investment, it just doesn’t make sense to retain debt, as the cost of debt is much higher than the benefits from savings.
To put it simply, the money that you save in a bank account is repackaged by the banking system and lent back to you at a much higher rate.
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Some savings are necessary, especially if there is an uncertainty about the security of your job. If you lose your job it may be difficult to get credit to live on, so the rule of thumb is to have enough savings to last at least 8-10 months of unemployment.
Some exceptions when debt is cheaper than savings is if you have a interest free debt or if there is a penalty attached to you paying off the debt. In such circumstances you will need to weigh up the gains versus the loss.