Saving for retirement is challenging, especially when money is tight. Nearly 60% of Americans say they live paycheck to paycheck, according to a survey from Charles Schwab, and finding cash in your budget to put toward your retirement fund can often feel impossible.

However, you don't need to make drastic budget cuts to save more for retirement. In fact, this one simple move can help you turn a few dollars per month into tens of thousands of dollars in savings by retirement age.

Young man holding hundred dollar bills in front of his face

Image source: Getty Images.

The smallest changes can make a big difference

It's easy to fall into the trap of thinking that if you don't have much to save, it's not worth saving at all. But boosting your savings rate by even 1% can make a significant difference down the road.

The average American starts saving for retirement at age 31, a report from Nationwide found. In addition, the median income among U.S. adults is approximately $48,000 per year, according to data from the Bureau of Labor Statistics.

Say you were earning $48,000 per year and saving 10% of your salary (or $400 per month). If you began saving at age 31 and were earning a 7% annual rate of return on your investments, you'd have $714,785 saved by age 67.

However, if you were to increase your savings rate by just 1% -- contributing 11% of your salary, or $440 per month -- you'd have saved $786,263, all other factors remaining the same. That's a difference of approximately $71,500.

Why you could save more than you think

While $71,500 is already a good chunk of change, there's a chance you could save significantly more than that without lifting a finger.

These calculations assume your income will remain the same from age 31 to 67, but in reality, your salary will likely increase as you get older. So even if you continue saving the same percentage of your income, the dollar amount you're contributing will increase -- which can cause your total savings to skyrocket over time.

In addition, if you're saving in a 401(k) and have access to matching contributions from your employer, you could stand to save even more. If you save an additional 1% of your salary and your employer matches those contributions, you could potentially double your total savings with no extra effort on your part.

Money is tight right now for millions of Americans, and saving for retirement may be low on your priority list. However, even if you don't have much to save, every little bit counts. By boosting your savings by just 1%, you can see an enormous difference in your total savings by the time you retire.