Social Security and Medicare are interrelated programs, so you might assume that the rules for both are the same. But actually, that's not true.

You can claim Social Security benefits at any age starting at 62. With Medicare, on the other hand, eligibility doesn't begin until age 65. And while you don't necessarily have to enroll in Medicare at age 65 exactly, in some cases, failing to do so could mean facing surcharges on your Part B premiums for life.

Meanwhile, seniors who are enrolled in Social Security and Medicare at the same time have their Part B premiums paid out of their monthly benefits directly. So for this reason, you may be inclined to sign up for Social Security ahead of Medicare. But doing so may not be the wisest idea, financially speaking.

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Don't sacrifice income for convenience

You may like the idea of being on Social Security at the time of your Medicare enrollment so your Part B premiums will be paid automatically. But while that might be a convenient way to pay those premiums, what you gain in that regard, you lose in monthly Social Security income.

You're not entitled to your full monthly Social Security benefit based on your personal income history until full retirement age (FRA) arrives. And FRA is either 66, 67, or somewhere in between, depending on the year you were born.

If you claim Social Security prior to reaching FRA, your monthly benefits will face a reduction, the extent of which will hinge on just how early you file. But for context, if you sign up for Social Security at 62 with an FRA of 67, you're looking at cutting your monthly benefits by 30%.

That's why you may want to wait until after you've enrolled in Medicare to sign up for Social Security. No matter what year you were born, you won't reach FRA prior to when you're eligible for Medicare enrollment.

Furthermore, Social Security allows you to delay your filing past FRA. And for each year you do, up until you turn 70, your benefits get an impressive 8% boost. A lift of that size could make it easier to afford your Medicare premiums throughout retirement.

Think carefully about your Social Security filing age

You might think that the easiest thing to do is sign up for Social Security ahead of Medicare, or even to sign up for both programs at the same time. But doing so could mean leaving yourself with a smaller Social Security benefit for life. And seeing as how your Medicare costs have the potential to climb over time, shorting yourself on Social Security could end up being a dangerous financial move that comes back to haunt you.

Of course, you may want to sign up for Social Security and Medicare at or around the same time if you've postponed your Medicare enrollment due to having group health plan coverage through a job. If you're first enrolling in Medicare at age 67, for example, at that point, you're already eligible for your complete monthly Social Security benefit because you're at your FRA. It's when you're looking at slashing your Social Security income that signing up for both programs simultaneously becomes more of an issue.