I have an eye-popping stat for you.

Credit card users voluntarily paid $12.5 billion in annual fees in 2016, according to Bloomberg. That's a little more than $39 for every man, woman, and child in the United States.

If you told me this a few years ago, I'd think it was just another case of consumer insanity. After all, the majority of credit cards are actually of the no-annual-fee variety. You almost have to go out of your way to apply for a card with an annual fee -- and that, I thought, was crazy.

But I've changed my view...

I used to think that it was illogical to pay any annual fees at all, but I've since come around. When used intelligently, annual fee credit cards come with cash back sign-up bonuses or travel rewards perks that more than compensate for the fee, or the hassle of closing the card before being charged a fee.

The Chase Sapphire Preferred is an excellent case in how signing up for an annual fee card can make sense. It charges an annual fee of $95, which is actually waived in the first year, but those who meet its spending requirements can cash in on a sign-up bonus worth about $625. Cancel before the first year is up and you'll never pay a fee at all.

The Chase Sapphire Reserve is even better. Although credit card users have to fork over $450 for the first year's annual fee, it offers the opportunity to cash in on two $300 annual travel credits and a 50,000 point sign-up bonus worth about $750. In all, an initial cash outlay of $450 results in travel perks worth as much as $1,350 in the first calendar year.

Compare the perks of these two annual fee cards with even the best no-fee cards and you'll see why paying a fee can make a lot of sense. We at Fool.com think BankAmericard Travel Rewards® is one of the best travel cards of 2017, partly because it doesn't have an annual fee. That said, its sign-up bonus of 20,000 rewards points (valued at $200 in travel statement credits) doesn't come close to the sign-up bonuses of cards with annual fees.

jar filled with U.S. currency of all denominations.

It can make sense to pay an annual fee for higher rewards. Image source: Getty Images.

Be smart and cash in

It's not just about the sign-up bonuses. It can make sense to pay an annual fee in exchange for a higher ongoing rewards rate, too.

Take the Blue Cash Everyday Card from American Express as an example. It offers 3% cash back on up to $6,000 of annual supermarket spending. A similar card, Blue Cash Everyday Preferred Card from American Express, carries a $95 annual fee but it offers up to 6% cash back on up to $6,000 of annual supermarket spending.

People who spend more than $3,166 at the grocery store each year would therefore benefit by paying the $95 annual fee to get 6% cash back rewards rate on their supermarket spending vs. the standard 3% rewards rate.

Of course, people who tend to carry balances on their credit cards should probably stay away from credit cards altogether, fee or no fee. And those who don't want to do the digging through the fine print of a credit card offer can find plenty of opportunities to score rewards with no-annual-fee cards.

But for the diligent credit card user, annual fees aren't necessarily something to avoid at any cost.

Jordan Wathen has no position in any stocks mentioned. The Motley Fool recommends American Express. The Motley Fool has a disclosure policy.