If you are paying for your own insurance, you may think you do not need to sign up for Medicare when you turn 65. However, not signing up for Medicare Part B right away can cost you down the road. 

You can first sign up for Medicare during your Initial Enrollment Period, which is the seven-month period that includes the three months before the month you become eligible (usually age 65), the month you are eligible and three months after the month you become eligible. If you do not sign up for Part B right away, you will be subject to a penalty. Your Medicare Part B premium may go up 10 percent for each 12-month period that you could have had Medicare Part B, but did not take it. In addition, you will have to wait for the general enrollment period to enroll. The general enrollment period usually runs between January 1 and March 31 of each year.

There are exceptions to the penalty if you have insurance through an employer or through your spouse's employer, but there is no exception for private insurance. The health insurance must be from an employer where you or your spouse actively works, and even then, if the employer has fewer than 20 employees, you will likely have to sign up for Part B. 

If you don't have an employer or union group health insurance plan, or that plan is secondary to Medicare, it is extremely important to sign up for Medicare Part B during your initial enrollment period. Note that COBRA coverage does not count as a health insurance plan for Medicare purposes. Neither does retiree coverage or VA benefits.

For a New York Times column about a man with private insurance who didn't realize he needed to sign up for Part B, click here.