# Credit Card Math: Easy Formulas to Pick the Right Card for You

Posted in Credit Card Rates • April 15, 2012

Having a tough time deciding between a low-APR credit card versus a rewards card, or figuring out whether it’s better to pay your taxes with debit or credit? Before you pick the card, spend a little quality time with your calculator. Using middle-school math, you can easily calculate which card works best for you.

## Rewards vs. Low Interest

To figure out whether you should go with a rewards card or a low-APR card, first calculate the rewards you’ll earn with the rewards card by multiplying the card’s rewards rate by an estimate of your annual spending. Written out as an equation, this looks like:

Rewards earned = rewards rate * annual spending

Then, figure out how many fees you’ll be paying for the rewards card by multiplying the card’s APR to your average balance, then adding other fees you’ll be charged on top of that.

Fees paid = (APR * average balance) + fees

If rewards earned is greater than fees paid, go with the rewards card. If not, the low-APR card is a better fit.

## Annual Fee vs. Lower Rewards

Many people instinctively avoid credit cards with annual fees, but that’s not always the best option; you may be giving up some pretty lucrative cash rewards. Before you commit to a no-fee credit card, do the math!

Choosing between a card with an annual fee versus a card with lower rewards can be done all in one equation — and the calculation even takes into account a possible waived first-year fee, and a difference in the signup bonuses of two cards.

To figure out the savings you’ll have with a card with an annual fee (Card 1) vs. a card with lower rewards (Card 2), first subtract Card 2’s reward rate from Card 1’s reward rate. Then multiply that by your annual spending, and then by the number of years you’ve held Card 1. This will give you the difference in the rewards earned over Card 1’s lifetime.

(Card 1 rewards rate – Card 2 rewards rate) * annual spending * years held

When you calculate the answer, put it aside for a moment.

Now, subtract the signup bonus you received from Card 2 from the signup bonus of Card 1. Write down that figure — call it Figure A.

Multiply the annual fee of Card 2 by the number of years you’ve paid the annual fee (usually the years you’ve held the card, minus one if the first year’s fee is waived). Do the same with Card 1. Then subtract the product you got from multiplying Card 2’s annual fee and the number of years you’ve paid the fee, from the product you got for Card 1. That will be Figure B.

Remember the signup bonus subtraction you did earlier? Take the figure you got (Figure A) and subtract it from the second figure you calculated (Figure B). The answer tells you the one-time difference in signup bonuses between Card 1 and Card 2, minus the difference in annual fees paid over the cards’ lifetimes. Here’s what the expression looks like:

(Signup bonus of Card 1 – signup bonus of Card 2) – [(annual fee of Card 1 * years of annual fee paid) – (annual fee of Card 2 * years of annual fee paid)]

You’re almost there.

Now, take the difference in the rewards earned over Card 1’s lifetime (the first answer you calculated) and add it to the one-time difference in signup bonuses between Card 1 and Card 2, minus the difference in annual fees (which is what you just found). Divide 1 by the sum that you calculate, and that will give you the savings with Card 1, the card with the higher annual fee, taking into account a possible waived first-year fee and difference in signup bonuses. You can use this figure to compare Card 1 with Card 2, and see which card will save you more money.

Interestingly, most credit cards with annual fees have higher payouts for a majority of rewards credit card holders. Do the math before you decide to pass over a card with an annual fee.

The whole expression written out looks like this:

1 / years the card is held * [ (Card 1 rewards rate - Card 2 rewards rate) * annual spending * years held + (signup bonus of Card 1 - signup bonus of Card 2) - (annual fee of Card 1 * years of annual fee paid - annual fee of Card 2 * years of annual fee paid) ]

## Paying Taxes: Debit Vs. Credit Card

The IRS allows you to pay taxes by credit or debit card — but which one should you choose, and how much will you save?

First of all, if your rewards rate is below 2 percent, don’t use the card. For payUSAtax.com, the minimum convenience fee is 1.89 percent.

If you choose to use a debit card, you’ll be charged a flat free. The lowest are from payUSAtax and Value Tax Payment, at \$3.49. To figure out whether you should pay, divide \$3.49 by your debit card’s rewards rate. If you’re paying more than that in taxes, go ahead and pay in debit.

Taxes you pay > \$3.49 / rewards rate (in percentages)

To see what it will look like to pay your taxes with your credit versus your debit card, try these calculations:

Rewards earned with credit = (rewards rate – 1.89%) * taxes paid

Rewards earned with debit = (rewards rate * taxes paid) – \$3.49

To compare the rewards earned with debit versus credit, add 1.89 percent of your debit rewards rate to the debit rewards rate and subtract the credit rewards rate from the sum. Then multiply that by the taxes you paid, and subtract \$3.49.

The calculation will look like:

Rewards earned with debit vs. credit = (debit rewards rate + 1.89% – credit rewards rate) * taxes paid – \$3.49

Remember: personal finance is about math as much as it is about psychology. Credit card companies rely on reams of data to figure out how much to charge you, how much to offer and whether to lend to you at all. You can match them equation for equation by focusing on the numbers, rather than the advertising.

This post was contributed by NerdWallet writer Ellie Wilkinson.

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