Social Security provides much-needed income for retirees, and it's especially valuable for those who can't afford to save much on their own for retirement. With the current federal minimum wage at $7.25 per hour, low-paid workers don't have much money to set aside for the future, making Social Security extremely important for the estimated 2.6 million workers who earn at or below that level. Social Security's way of calculating benefits does a lot of good for low-income earners, but it still leaves poorer retirees in a tough situation. Let's take a closer look at how much someone earning the minimum wage can expect to receive from Social Security.

Image source: Getty Images.

What minimum-wage earners pay in Social Security taxes

That Social Security Administration starts assessing payroll taxes from the first penny of earnings, so even minimum-wage workers aren't exempt from paying them. If you earn $7.25 per hour for 40 hours a week, 52 weeks a year, then your annual salary will add up to $15,080. You'll pay 6.2% in payroll tax on that amount, which works out to $934.96. Your employer will also pay an equal $934.96 amount on your behalf.

There is a wage limit above which Social Security taxes are no longer due. However, that limit is far above the minimum-wage level. All of a minimum-wage worker's earnings therefore show up in their work history for the purpose of determining their retirement benefits.

What minimum-wage earners get back from Social Security

One thing to remember is that Social Security doesn't base your benefits on a particular year or two of earnings. If you earn minimum wage for a short period of time but then get a higher-paying jobs, then your benefits will rise. Social Security takes your 35 highest-earning years after adjusting for inflation, and it then takes the monthly average of that amount over that 35-year span as the starting point for determining your monthly benefit check.

However, many minimum-wage workers have difficulty advancing in their careers, so we'll make some assumptions that reflect that unfortunate reality. Take someone who will turn 62 in 2017, who earns the current minimum wage, and whose earnings have risen at the rate of inflation throughout a 35-year career. In reality, minimum wage has gone up in bigger chunks at irregular intervals, but this scenario will be easier to calculate in order to generate a baseline number.

A minimum-wage worker in this hypothetical scenario would have average indexed monthly earnings (AIME) of $1,257 per month. To calculate their Social Security benefits, we'd use the SSA's formula. First we take 90% of the first $885 in monthly earnings and then add 32% of earnings above $885. That requires two calculations: 90% of $885 is $796.50, and 32% of the remaining $372 is $119.04. Add those two figures up, and you get $915.54 per month, which is the benefit this person would be entitled to receive at their full retirement age in 2021.

However, many minimum-wage workers can't afford to wait until full retirement age for their benefits. For them, claiming at the earliest possible age of 62 comes with a price: a big reduction in benefits. This reduction depends on when you were born, but for those turning 62 next year, filing early would cost you more than $235 per month, producing a benefit check of around $679. By contrast, if you are somehow fortunate enough to be able to wait until age 70, then you'd get an extra bump to your benefits, bringing you close to $1,200 per month due to delayed-retirement credits.

Why Social Security is so important to low-income earners

You can see from the numbers above that Social Security plays a large role in replacing the earnings of minimum-wage workers. That $915.54 per month adds up to nearly $11,000 per year in Social Security benefits, and that's almost three-quarters of what full-time minimum-wage workers earn. That said, that missing one-quarter of earnings is still a massive problem for most retirees who worked minimum-wage jobs, because they typically had little opportunity to accumulate savings for retirement.

Social Security has a progressive design, which means it benefits low-earning workers more than high earners. That may not seem fair to higher-income workers, but it's a lifesaver for those who earn minimum wage. By providing continued basic living expenses in retirement, Social Security takes on a key role in the welfare of those Americans who need it most.