Is there a particular formula used to determine when it is financially beneficial to pay off a home equity loan of 8.25 using a credit card of 3.99?

Ignoring taxes (which may or may not come into play anyway) for a moment: The interest rate, which is the cost of boworring the money, is identified. The lower the rate, the financially better. Simple. But, I'll bet the low Cr Card rate is for a short period, like 6 months, after which it may become much, even several times higher than the HE loan, (which is probably for a payout over many years). Presumably your not expecting to pay off the loan when the rate changes, and as the Cr Card would likely turn out to NOT be the rate your saying here over the entre period you would keep the loan, it would be much higher = financially bad. You also can consider that many Cr Cards have transfer fees, etc. which, like fee's to establish a credit line, work to increase the rate you ultimately pay. Finally, if the HE loan qualifies (there are a number of conditions that need to be met), as a tax deductible mortgage, the rate is effectively lower by the added income tax savings you enjoy. (Of course you only get this if you itemize deductions to start). Say you pay income tax at a 25% rate ($25 for every $100 of taxable income). A rate you need to calculate for yourself, as it changes for everyone and situation. Then, if the HE loan is deductible (the Cr Card one can't be, as it isn't secured by the residence), for every $X of INTEREST (not the principle portion of the payment, only the interest portion), the income tax you would normally pay is lowered by that percentage, so compared to not getting any deduction, it's like getting a lower interest charge.