The decision to file for Social Security isn't an easy one. The age you claim benefits at will determine how much monthly income you collect throughout retirement, and it's therefore not a choice to take lightly.

You can first sign up for Social Security at age 62, and once you turn 70, you shouldn't hold off any longer because there's no financial incentive to do so. As such, 70 is usually considered the latest age to claim Social Security, even though you're not forced to sign up at that point.

Smack in the middle of that window are two other important milestones: age 65, when Medicare eligibility kicks in, and ages 66 to 67, which is when full retirement age (FRA) begins. FRA is when you're entitled to your full monthly Social Security benefit based on your earnings history. If you file before FRA, your monthly benefit will be reduced on a lifelong basis.

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As such, the decision to sign up for Medicare is a much easier one. If you need a health plan, you enroll in the seven-month window around your 65th birthday to secure coverage, and if you're still covered by a qualified group health plan at age 65, you can sign up for Medicare at a later point in time without penalty.

Many seniors, however, wonder if it makes sense to sign up for Medicare and Social Security at the same time. And here's why that's not such a bad idea.

Social Security at 65: a nice middle ground

The problem with claiming Social Security early is reducing your benefits in the process. That's a dangerous move for anyone with little to no retirement savings in particular, and if you sign up for Medicare and Social Security at the same time, it means you're filing early, no matter what your FRA looks like.

The reality, however, is that many seniors rush to claim their benefits as soon as they turn 62, making that the most popular age to sign up. Part of that boils down to recipients being pushed out of the workforce sooner than expected, while part of it comes down to impatience. And then there's the nagging fear that Social Security is in the process of going bankrupt (which it isn't) that's likely driving seniors to snag their money as soon as they can, before it goes away.

But claiming Social Security at 62 means slashing your monthly benefit by anywhere from 25% to 30%, depending on your precise FRA. That's a pretty large hit to grapple with for the rest of your life.

On the other hand, signing up for Social Security and Medicare at the same time means claiming benefits just one to two years early. That may not be ideal if you're really lacking in savings, but it's also not nearly as terrible as signing up four to five years early.

Enrolling in Medicare and Social Security simultaneously

If you claim Social Security at 65 with an FRA of 66, your benefits will be reduced by 6.67%. And if your FRA is 67, you're looking at twice that reduction -- 13.34%. And this way, you sort of arrive at a compromise -- you get your money without having to wait too long, but you also don't slash your benefits to the largest extent possible.

Signing up for Medicare and Social Security at the same time also comes with one key upside -- paying your Medicare Part B premiums directly out of your benefits, which happens automatically. Not only does that mean not having to worry about paying those premiums yourself, but it also means getting to benefit from Medicare's hold-harmless provision, which prevents your Social Security benefit from going down when a Part B premium hike exceeds your cost-of-living adjustment (COLA).

Medicare costs can climb from year to year, and Social Security benefits are eligible for a yearly raise, or COLA. If you're on Medicare without Social Security and your Part B premiums go up by $15 a month, you're liable for that whole $15. But let's say you're on Social Security and your COLA for that same year is only $12. Paying the full extra $15 for Medicare out of your benefits would leave you with a lower monthly payment from Social Security than you've been getting, and that's not allowed. As such, you'd only, in this scenario, pay an extra $12 for Medicare, so that's a modest perk.

Though it often pays to hold off on claiming Social Security until FRA or beyond (you can boost your benefits by delaying them up until age 70), if you really can't wait that long, filing at 65 is a reasonable alternative. That way, you can sign up for Social Security and Medicare at the same time and enjoy some convenience and potential cost-savings on premiums without slashing your benefits too substantially.