Most people should sign up for Medicare when they reach 65; if they wait until later, they have to pay a significant penalty when they do sign up. There’s an exception, though, for people who are still employed at age 65 and are covered by a group health plan. These people can delay signing up for Medicare without a penalty.

But here’s a common problem: Suppose you’re no longer working when you turn 65, but you’re still covered by your old employer’s group health plan under COBRA?

COBRA is a federal law that allows many workers to continue on their employer’s health plan for up to 18 months after their employment is terminated or their hours are reduced.  

Many people assume that they can delay signing up for Medicare if they still have COBRA coverage when they turn 65. But that’s not true. If you’re no longer employed when you turn 65, you have to sign up for Medicare Part B or you will face a penalty, even if you still have COBRA coverage.

The penalty for delaying can be very significant – there’s a 10 percent premium penalty for each year that enrollment is delayed. For example, if you turn 65 in 2012 but wait until 2014 to enroll in Medicare, your monthly Part B premium will be 20 percent higher than the standard premium…and this will be true for the rest of your life.

The rules for signing up for Medicare Part D, which covers prescription drugs, are a little different. People who aren’t employed when they turn 65 but still have COBRA coverage can delay signing up for Part D without a penalty, but only if the prescription drug plan they have under COBRA amounts to “creditable coverage,” which means that it’s expected to pay on average as much as the standard Medicare Part D plan.

The penalty for delaying enrollment in Part D is also more complicated; it’s calculated by multiplying 1 percent of the national base premium by the number of months that you were without creditable coverage.

The Medicare enrollment period begins three months before your 65th birthday, and continues for seven months.