We hear a lot about the importance of saving for retirement, and how the earlier we start, the more time our money has to grow. But some people make the mistake of curbing their savings as they get closer to retirement.

The logic goes something like this: Since there's not much time to generate a return on money invested a year or two prior to retirement, there's less value in saving it. Plus, for many older workers, retirement savings often play second fiddle to more seemingly pressing obligations and temptations, like paying off a mortgage or helping grandchildren with college. But in reality, your last few working years are a great time to not only save, but save like you've never saved before.

Every last dollar counts
The average American household approaching retirement has just over $100,000 saved, which may sound like a lot at first. But let's assume you have $100,000 saved for retirement, and that you live another 20 years once you stop working. Let's also imagine that your investments generate an average annual 4% return in retirement. (Remember, by then, you'll want to mostly stay away from riskier, high-yield investments like stocks and keep much of your money in lower-yielding vehicles like bonds, whose returns won't be as high.) In our scenario, you'll be able to withdraw about $600 a month during retirement.

Now let's factor in Social Security. The average monthly benefit is currently $1,341, so if we take that amount and add $600 from retirement savings, you'll be left with $1,941 a month to live off. How does that sound? If the answer is "not good," then it's time to ramp up your savings while you still have a few working years left.

While you might think that contributing money to your retirement account late in your career won't do much in the long run, the truth is that every little bit counts. Imagine that instead of foregoing retirement savings during your last two years of full-time work, you push yourself to save $10,000 each year, or $20,000 in total. If we apply that same 4% return, your additional savings will give you an extra $126 per month over the course of a 20-year retirement -- and that can go a long way.

There are benefits to saving, too
Here's another reason to increase your savings as retirement looms. If you're earning more money now than you did earlier on in your career (which is the case for many of us), then you're also most likely paying higher taxes than you were in years past. By putting money into a 401(k) or IRA, you'll lower your taxes at a time in your life where your IRS burden may be at its highest. For 2016, anyone 50 or older can contribute up to $24,000 to a 401(k) or $6,500 to a traditional IRA.

Better yet, if your company offers a matching program, you'll come out even more ahead. Let's say your employer will match 3% of your total contribution amount. By putting $24,000 a year into a retirement account, you'll not only get to reserve that money for when you need it the most, but you'll also snag another $720 courtesy of your employer. That's $720 in free money for every year you max out those contributions.

While it's smart to use your last few years of earnings as an opportunity to eliminate debt, pay off your mortgage, or upgrade high-cost items like your car or appliances while you still have the income, don't make the mistake of shoving your retirement savings into the backseat along the way. Once you stop working, you'll be limited to a fixed income, and you'll have far less financial wiggle room than ever before. The more money you save while you still can, the better off you'll be in the long run.