The millions of seniors who buy Medicare supplements may be charged wildly different amounts — even when they’re the same age, living in the same city, and getting precisely the same benefits, Weiss Ratings reports.

The reason: The commercial insurers that offer the supplements are allowed by state regulators to charge based on their expenses and costs of present patients.

One example: A 79-year-old woman in Aventura choosing Plan F — a comprehensive plan covering almost all out-of pocket Medicare costs — could pay anywhere from $3,654 a year to $5,419 for exactly the same protection, according to Gavin Magor, an analyst with Jupiter-based Weiss Ratings, an independent rating agency of financial institutions.

About 10 million seniors choose to sign up annually for these supplements, according to America’s Health Insurance Plans. That process begins Saturday, with the start of Medicare’s annual open enrollment.

The supplements, known as Medigap policies, help seniors with the co-pays and health expenses that standard Medicare doesn’t cover — expenses that can run into the tens of thousands of dollars for a severe illness.

“I love my supplement,” says Barbara Waks, a 79-year-old in Aventura who says she pays $3,348 a year for a United American policy. “It’s very expensive, but it’s wonderful. I’ve been with them forever. They never question the bills.”

The problem is that’s it extremely difficult to get the best price. “This is a huge example of buyer beware,” says Richard Fiesta of the Alliance for Retired Americans. “Price differences vary greatly from plan to plan and state to state.”

In the 1970s and 1980s, the situation was even worse, Fiesta said. The federal government then standardized the supplements. At present, there are 10 plans — each offering exactly the same benefits, with the cheaper ones covering less out-of-pocket and the most expensive covering virtually everything.

The most popular is the most expensive: Plan F, which picks up essentially all out-of-pocket costs. Forty-seven percent of those buying supplements choose Plan F, according to AHIP.

The plans are offered by commercial insurance companies. Their rates generally need to be approved by state insurance regulators, and like other types of insurance, they can vary by location and age — and the insurer’s costs.

“It’s literally like buying a Coke,” says Magor at Weiss Ratings. “Every Coke is the same, but the price can be a lot different from one store to another.”

Wayne Stetler, an independent insurance agent in Virginia who is also licensed in Florida, says that, like other insurances, the companies with the largest customer base tend to offer the best rates because they can do a better job of spreading risk.

“That’s why AARP usually has the best rates in Florida — because they have the biggest pool,” says Stetler, who specializes in selling Medigap policies.

But there can be considerable discrepancies. After analyzing 5.6 million premium rates of 165 insurers nationwide, the Weiss survey, which analyzed more than 5.6 million premium rates of 165 insurers nationwide, found even with a single plan, the highest premium could be 13 times more than the cheapest.