[free hotel night POINTS0416]Matthew Wakem In On Points, Brian Kelly, founder of The Points Guy, shares his strategies for getting the most out of your points and miles. There's a saying, "cheap is expensive." And it definitely applies to credit cards. Often, cards with no or low annual fees offer few perks. It can make sense to pay an annual fee — even a hefty one — for certain cards, because their benefits make up for the cost many times over. I devoted an entire column to the Southwest Companion Pass, which can save travelers _thousands_ of dollars a year. Here's another weapon for your travel arsenal: the Citi Prestige card. The Prestige was launched in the U.S. in 2014 to compete with the American Express Platinum card. Like the Amex, it has a $450 annual fee. Off the bat, Citi Prestige gives cardholders $250 in airfare rebates, American Airlines Admirals Club access (a $500 value), three points per dollar spent on airfare and hotels, and two points on dining and entertainment. But by far the most valuable benefit is the fourth night free on hotel stays. That perk has already saved me thousands of dollars this year. This benefit is ridiculously generous, especially if you like luxury hotels. It's easy to use, too: book your hotel stay through the Citi Travel Concierge, put the charge on your card, and the fourth night is free, even if it is more expensive than the first three. I was skeptical at first, figuring that Citi inflated hotel rates to make up for the bonus, but they don't. Citi uses Carson Wagonlit to book hotel stays for Prestige cardholders, so you can check rates on their website. The concierge should quote you the same price. If you have a AAA membership or see a better rate somewhere online, you can request that price — in many cases the concierge can book discounted rates that don’t show up in the system. The fourth night gets refunded after the stay as a statement credit. You can also add your loyalty program details and in most cases get loyalty points and elite credits. And since the fourth night free shows up as a statement credit, if someone else pays for your stay (like a reimbursement for business travel) you can basically make money on your hotel stay. Note that you can only earn one free night per reservation, so for an eight-night trip you'll only get one free. If you book two four-night reservations you'll probably get two separate statement credits unless the hotel combines the reservations. I just got the Citi Prestige in January, but I've already put it to the test on two trips. The first was a four-night stay at the Dean Street Townhouse in London where the room rate for the first two nights was 255 GBP and the last two were 360 GBP (about $505). Two weeks later I got a credit for $505 to my account — more than the annual fee in a single stay! This summer I'm staying at the chic Belvedere Hotel in Mykonos, Greece, where I'm splurging for a special occasion. My total for the stay is €3,800 (a little over $4,000); the fourth-night credit (including taxes) is $1,054, bringing the total down to $3,134.28. In both cases I checked online rates and the Citi Concierge was able to book me the absolute lowest rate available for the room type I wanted. Considering all the perks — I didn't even get into the three free golf games a year—and the current 50,000 point sign-up bonus (worth $800 in American Airlines airfare), the Citi Prestige is earning its keep in my wallet. MORE FROM TRAVEL + LEISURE: * Everything You Need to Know About Planning a Cruise Vacation * The Next Great Honeymoon Destinations * This Year's Top Tourist Attractions NOW WATCH: A lavish Indian palace was just ranked the number one hotel in the world by TripAdvisor