Editor's Note: APYs listed in this article are up-to-date as of the time of publication. They may fluctuate (up or down) as the Fed rate changes. CNBC will update as changes are made public.

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It's generally a smart idea to plan for the unexpected, whether that's medical bills, a sudden job loss or an immediate car repair.

Emergencies are bound to happen, and once they do, you'll want to have the means to cover these expenses and protect yourself from a financial setback. That's why experts advise people to set aside money in an emergency fund, especially when job security is on the forefront of Americans' minds.

But while Sallie Krawcheck, co-founder and CEO of the digital investment platform Ellevest, is all for having an emergency fund to fall back on, she doesn't believe it's worth delaying your credit card debt for.

"My theory comes down to money — saving money," Krawcheck tells CNBC Select. Credit cards charge high interest rates, so cardholders are in fact paying to borrow money when they carry a balance.

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"Every single day your high-interest debt goes unpaid, it's costing you money — a LOT of money — in interest," Krawcheck says.

Instead of putting your extra cash toward an emergency fund, she suggests that focusing all of it on credit card debt first will save you more in the long run.

Let's take a look at a hypothetical example that shows how fast credit cards' compound interest makes your unpaid debt grow:

If you had a credit card balance of $6,194 and were charged a 15.78% interest rate, paying only $200 per month toward that debt would take you over three years to completely pay off the credit card. In that time, you would spend $1,812 in interest alone — bringing your grand total to $8,006 ($6,194 + $1,812).

However, this is better than the alternative, argues Krawcheck: If you instead used that monthly $200 payment toward building an emergency fund from scratch in a high-yield savings, such as the Varo Savings Account with an APY of 1.20%, three years would yield you a lesser $7,336 total — not to mention, you'd still have debt.

"You might as well take money you're saving and throw it out the window," Krawcheck says.

Plus, paying down your credit card debt first improves your credit score because it lowers your credit utilization rate (CUR). The lower your utilization rate, the better your credit score because it shows you aren't using up all of your credit and not paying it back. Credit utilization makes up 30%, or one-third, of a credit score on the FICO model.

So while the general rule of thumb is to have three to six months' worth of savings set aside before conquering debt, remember that interest will cost you in the meantime.

Bottom line

While building an emergency fund can feel like you're doing something right, it instills a false sense of momentum if you are forfeiting money to credit card interest to do so, argues Krawcheck. Saving may be important if you worry about losing your job and paying for high-priority bills, but it is going to cost you more over time.

To feel a sense of positive momentum as you pay off this debt, Krawcheck suggests carrying around an index card in your wallet and checking off when you pay off a chunk of debt. And if you have a sudden emergency come up, then use a credit card to pay for it. This way, you're incurring high interest on an outstanding balance for a much shorter period of time.

Don't miss: 61% of Americans will run out of emergency savings by the end of the year—here's how to reduce expenses now

Information about Alliant Cashback Visa® Signature Credit Card has been collected independently by CNBC and has not been reviewed or provided by the issuer prior to publication.

Editorial Note: Opinions, analyses, reviews or recommendations expressed in this article are those of the Select editorial staff’s alone, and have not been reviewed, approved or otherwise endorsed by any third party.