Social Security is vital for the financial health of Americans, but it's also an extremely complicated program. The manual that Social Security's own employees use is hundreds of pages long, and it's full of obscure rules that can trip up even those who know Social Security inside and out. It's therefore not surprising to find that millions of people make mistakes in dealing with Social Security that end up costing them money.

A lot of the debate about Social Security has centered on how decisions about the age at which you start collecting monthly benefit checks can have an impact on what you get from the program over the course of a lifetime. Those arguments are valid, and in some cases, one decision can indeed have a sizable advantage over another. However, there's one costly Social Security mistake that many people make that's indisputably something to avoid -- and at the same time particularly easy to stop from happening.

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Dealing with the death of a spouse

One of the most confusing parts of Social Security has to do with how a person's own retirement benefits interact with the benefits you're entitled to get as the spouse of another Social Security recipient. In most cases, while your spouse is still alive, you're entitled to receive the greater of what your own retirement benefit would be or what you're entitled to receive as a spousal benefit based on your spouse's work history. You typically aren't allowed to claim one benefit while letting another continue to grow, as law changes over the past several years have just about taken away that right for new retirees. Instead, you're deemed to collect both your own retirement benefit and any spousal benefit to which you're entitled at the same time.

The way Social Security benefits work changes after the death of a spouse. At that point, survivor benefits kick in, giving you the right to collect an amount based on what your spouse was receiving in retirement benefits at death. Indeed, survivor benefits tend to be available earlier than your own retirement benefits, with surviving spouses becoming eligible to claim survivor benefits when they turn 60, rather than the 62-year-old minimum for retirement benefits.

For whatever reason, survivor benefits don't interact with retirement benefits the same way that spousal benefits do. It's true that if you claim both benefits at the same time, you'll still receive whichever amount is greater. However, unlike most other benefits, a surviving spouse can choose to elect to receive just one of those benefits and delay claiming the other benefit. As you'll see below, failing to take advantage of that opportunity can be extremely costly.

Would you want to give up $763 a month in extra benefits?

To see how this can play out in real life, take a simple example. Say you're a surviving spouse born in early 1957 who just turned 62 and has a work history that will provide retirement benefits of $1,600 per month at full retirement age, which is 66 1/2. Based on your deceased spouse's work history, you could also claim survivor benefits of $1,600 per month at full retirement age.

If you claim both benefits now, then both will be reduced to account for filing for benefits early. The reduced survivor benefit would be $1,285 per month, while the reduced retirement benefit would be $1,160 per month. Social Security would just pay the larger of the two, giving you a single $1,285 payment per month.

However, you can just claim your survivor benefit now while letting your retirement benefit keep growing. You'd still get $1,285 per month from the SSA now. But you could then claim retirement benefits later on at full retirement age and get $1,600 per month -- $315 more than you'd get now. Alternatively, you could wait until you turn 70 and get $2,048 per month thanks to delayed retirement credits. In other words, you could boost your future monthly payment by as much as $763 -- without giving anything up now.

Don't make this mistake

The sad thing is that many Social Security recipients make this mistake every day. Even if you consult directly with the SSA for help on your claiming decision, you can't afford to count on them to help you avoid making the wrong choice and costing yourself tens of thousands of dollars over the course of your lifetime.

If you've lost your spouse, understand that the implications of claiming Social Security are more complicated than you might expect. By getting help not just from the SSA but also from reputable advisors, you can make sure you get every penny from Social Security that you deserve.