Most people who try and save while they're in debt are simply throwing their money away; even if the debt is a mortgage.
The amount of interest you pay to borrow is much more than you earn on your savings, so pay the debt off with your savings and you're quids in.
How much?
Someone with $5,000 on a credit card and $5,000 saved is likely to be $700 a year better off by paying off the debt with the savings. This is a typical example of how most people can save just by looking at how much of their debt can be paid off.
Another thing you should explore is how much other banks will pay you in interest if you moved your account over to them. In credit card business, loyalty does not pay - most providers give great introductory rates to new customers. So simply by closing your account and re-registering could net you anything around $200 a year.
In this hard economic times, it's worth shopping around for better credit card rates than what your current provider is offer.
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