The best cash back credit card if you like to keep things simple

A flat-rate cash back credit card is a great choice for anyone who wants to save big without having to worry about strategic shopping or taking advantage of specific rewards. But some flat-rate cards are better than others.

To determine which one is the best, CNBC Make It analyzed the most popular cash back offers in the U.S. Using a sample budget based on spending data from the Bureau of Labor Statistics, we estimated how much money each card would save you after five years, while accounting for bonuses and annual fees. We also considered other characteristics that could set a card apart, such as interest rates and introductory offers.

Based on the data, here is our No. 1 choice for the best flat-rate offer out there. It's also the runner-up to our pick for the best cash back card overall: the Chase Freedom. But if you want to keep things simple, we recommend you go flat-rate.

The Double Cash offers a flat rate of 2 percent cash back on all purchases: 1 percent when you shop and 1 percent when you pay your bill.

It requires no annual fee, offers a $100 sign-up bonus and promises a 0 percent introductory APR for 18 months, providing users an opportunity to pay off debt. What's more, unlike many popular cash back cards, the Double Cash has no rewards cap, so if you spend big one quarter, the savings don't stop piling in.

Just be sure to redeem your rewards if you stop using the card. They will expire if you don't earn any cash back over 12 months.

• Cash back: 1 percent on purchases and 1 percent when you pay off your bill
• Annual fee: $0
• Bonus: $100 if you spend $500 within first 3 months
• Introduction APR: 0 percent for 18 months on balance transfers
• Variable APR: 14.99 to 24.99 percent based on your credit score
• Foreign transaction fee: 3 percent
• Estimated return after five years: $1,870

The Double Cash tops popular 1.5 percent cash back offers from popular cards such as the Chase Freedom Unlimited, the Capital One Quicksilver and the Wells Fargo Cash Wise Visa.

There are some cards, however, that match the 2 percent offer, like the Fidelity Rewards Visa Signature. But with that card, users only get 2 percent if they deposit their cash back into a Fidelity savings account. That's nice if you're interested in automating your finances but it also leaves you with less flexibility and control.

The PayPal Cashback Mastercard for PayPal members, meanwhile, also offers 2 percent cash back, but unlike the Double Cash, it doesn't have a sign-up bonus or introductory offer.

A third competitor, the Alliant Cash Back Visa Signature Credit Card, offers an even higher percentage: 3 percent cash back the first year on all purchases and 2.5 percent thereafter. But this card is only accessible to Alliant Credit Union members, it doesn't have a sign-up bonus and it charges a $59 annual fee after the first year. Plus, it's for big spenders. As advertised, it's "exclusively designed for those spending $50,000 [or more] a year on their card."

So all things considered, the Double Cash is our No. 1 choice not just because of its high 2 percent flat-rate, sign-up bonus and introductory APR offer, but because it is easy to use and highly accessible as long as you have a good credit score.

To determine which card offers the best flat-rate cash back deal, CNBC Make It vetted highly rated cash back cards based on their cash back offers, introductory and eventual APRs, annual fees, bonuses, recommended credit scores, late fees, balance transfer fees, foreign transaction fees, redemption options and customer reviews.

We then estimated how much money each card would save the typical American after one year, two years and five years. Our assessment heavily weighs the five-year return to avoid a large sign-up bonus skewing the results. We also assume that most people want a great card that they can stick with for years, especially since bouncing from card to card can be bad for your credit score.

To estimate the return, we used expenditure data from the Bureau of Labor Statistics to make a sample budget broken down by average annual spending in categories like gas ($1,909), groceries ($4,049), dining out ($3,154) and general purchases ($10,529). The general purchase category includes shopping, entertainment, public transit and vehicle expenses other than gas.

The estimate incorporates bonuses and assumes you have a high credit limit and that you use your card for 90 percent of the purchases you make in these categories, accounting for instances where you have to use cash or shop somewhere that doesn't accept your card.

Once we had our estimates, we then weighed cash returns against other factors including interest rates and fees, cash-back categories, practicality, bonuses and other perks.

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