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New-car buyers often have a choice of incentives, and it’s best to run the numbers to see which yields the better long-term deal.

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Consumer cash rebates have been a part of the U.S. automotive landscape since the 1970s, and they’ve become valuable tools to help boost sales of slower selling models. Rebates have since been joined by cut-rate financing deals that are often used instead of, or sometimes in addition to, cash-back deals.

Automakers have been heavily leaning on such incentives in recent years, with the industry-wide average having risen for three consecutive years to over $3,700 per vehicle as of this writing.

They often vary by region in order to address local supply and demand issues, so be sure to see what’s being offered in your area of the country by checking any of the automakers’ websites and clicking on a “special deals” or “local offers” tab, which is usually at the bottom of the home page.

While in some cases it can be a better deal to take the cash rebate up front, there are times when it’s advantageous to choose a discounted financing offer instead. Here’s how to decide which is best.

Consumer cash rebates are paid directly to the buyer and are usually applied directly to the down payment. This can be especially beneficial for buyers struggling to make a down payment or who are looking to pad the amount they can put down to minimize monthly payments, or to qualify for more favorable loan terms. Of course, if you’re paying cash for a car or truck, this is the only way to go.

In addition, specific incentives are sometimes given to returning customers trading in a same-brand vehicle or those coming out of a competitor’s model; sometimes small rebates are further offered to military personnel, recent college graduates, or members of select organizations like the AAA.

As an alternative, buyers can usually take advantage of discounted financing, with interest as low as zero percent and terms as long as 84 months, depending on the model. Generally speaking, the costlier the car or truck, the better a cut-rate financing deal becomes, simply because there’s more money at stake to save. On the down side, such deals are usually reserved only for those having pristine credit histories; those having lower FICO scores will pay higher rates.

Here’s how things stack up with a vehicle having a $60,000 purchase price with a choice of a $2,000 rebate or zero percent financing for 60 months, and the buyer making an $8,000 down payment: Taking the cash up front and financing at 3 percent results in a monthly payment of $898 and a total out-of-pocket of $53,906, while taking zero percent financing will yield a $867 payment and $52,000 total outlay. The advantage here goes to the cut-rate financing by a whisker.

And here’s how things look if we boost the cash rebate amount to $5,000: The $30,000 vehicle with a $5,000 rebate and $5,000 down will yield a $359 monthly payment and $21,562 total outlay over five years, versus a costlier $417 a month with $25,000 paid at zero percent interest. Meanwhile, taking a $5,000 rebate and putting $8,000 down on a $60,000 model will set a buyer back $773 a month and $47,359 after five years at 3.0 percent, versus $867 a month and $55,000 out of pocket taking the zero percent financing. In these cases, more cash-back yields the better deal.

Sometimes, automakers offer both cash back and cut-rate financing as an alternative to a bigger rebate. We’ve seen offers as a combined $3,500 cash back and zero percent financing as an alternative to a $5,000 rebate.

Unless one is paying cash, or a poor credit rating disqualifies you, taking a combined rebate and financing deal almost always yields the best long-term savings.

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Transportation reporter

Andrew covers transportation, real estate, casinos and other topics for The Times business section. A Crown Point native, he joined The Times in 2014, and has more than 15 years experience as a reporter and editor at Region newspapers.