Many seniors end up relying quite heavily on Social Security to cover their living costs once they leave the workforce behind. And that extends to those who manage to come into retirement with a decent chunk of savings.

For this reason, it's a good idea to squeeze as much money out of Social Security as you can. And the simple act of working one extra year could help you boost your monthly benefits substantially.

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The upside of working a year longer

Many people land on a specific retirement age and decide to stick to it. And so if you decide to retire, at, say, age 67, which may be your full retirement age (FRA) for Social Security purposes, the idea of then having to work until age 68 may not sit all that well with you. But if you want to snag a higher monthly Social Security benefit for life, putting in those extra 12 months could make a huge difference.

The longer you wait to claim Social Security, the higher a benefit you'll lock in -- up to a certain point, which is age 70. But delaying your filing a single year past FRA, for example, will give your benefits an 8% boost. And working an extra year could make it possible to hold off on signing up so you can snag that increase.

Meanwhile, if you're looking to claim benefits before FRA, you should know that filing early will result in a lifelong reduction. So, let's say your FRA is 67, but you're looking to retire at age 66. If you push yourself to work one extra year and hold off on claiming Social Security, you'll grow your benefits by 6.67% by virtue of not facing that reduction.

But that's not the only way an extra year in the workforce might raise your benefits. The monthly benefit you get from Social Security is calculated based on your highest 35 years of wages. But if you're able to replace a year of lower wages with higher ones, you'll lock in a higher benefit in the process.

So if you're 67 years old and all set to retire, only you're now earning more money than you've ever earned before, if you work 12 additional months, you'll replace a year of lower earnings with higher earnings, thereby raising your benefit.

It pays to push yourself

At some point, you can and should decide that you've put in your time in the workforce and are officially done holding down a job. But if you have any financial concerns going into retirement, it pays to consider the upside of delaying that milestone by a single year.

In addition to scoring a higher Social Security benefit, working a year longer should make it possible to leave your savings untouched for an extra 12 months. You also might manage to add to your IRA or 401(k) plan, thereby giving yourself an extra cushion that could come in very handy once you officially stop working.