Medicare eligibility begins at age 65, and you can first enroll up to three months prior to the month of your 65th birthday. But many seniors find that they're still working at 65, and as such, already have health coverage at that time. If that's the case, you don't need to sign up for Medicare right away -- but it could pay to do so.

How Medicare works with other insurance

You are allowed to have Medicare in conjunction with another health insurance plan. In fact, in some cases, it could be beneficial. If you're 65 and have health insurance through an employer, you can sign up for Medicare Parts A and B at that time, or just Part A.

Doctor talking to smiling older woman

IMAGE SOURCE: GETTY IMAGES.

Part A is what pays for hospital care, and it's generally free for enrollees -- meaning, you don't pay a premium for it. Part B covers outpatient services and diagnostics, and there is a premium attached to it. Currently, that premium costs $144.60 as a baseline, but it can cost more if you're a higher earner.

You'll often hear that if you don't sign up for Medicare on time (meaning, in close proximity to your 65th birthday), you'll risk lifelong surcharges on your Part B premiums. But that only holds true if you don't have access to a group health at age 65 through an employer with 20 or more employees. If you have that group health plan, you'll get a special enrollment period to sign up for Medicare once you leave your employer or your group health coverage ends -- whichever comes first.

Now, let's assume you have a decent group health plan at work, and your employer has that 20-person minimum. In that case, what you may want to do is sign up for Medicare Part A at 65, since it's free. That way, it can serve as your secondary insurance in the event you wind up needing hospital care and your primary insurance (your group health plan through work) doesn't pick up the entire tab. You can even choose to take Part B while having a health plan already, and it can serve as secondary insurance for you as well -- but you'll need to pay for it.

Does it pay to have Medicare plus another health plan?

If your group health plan through work isn't all that comprehensive, then it could pay to get coverage under Medicare simultaneously -- or at least sign up for Part A, since it doesn't cost you anything. The only drawback to going this route is if you're participating in a health savings account (HSA), you can no longer make contributions once you're enrolled in Medicare. HSAs offer a host of tax benefits (similar to those you'd find in popular retirement savings plans like 401(k) and IRAs), so that may be a perk you're hesitant to give up -- especially if your employer makes HSA contributions on your behalf, effectively giving you free money to pay your healthcare costs.

When it comes to signing up for Medicare while already having health insurance, there's really no right or wrong answer. But you should know that doing so is an option, and one that could benefit you.