Retirement costs the average senior $46,000 a year, while Social Security pays the typical beneficiary about $18,000 annually. Do the math, and it's clear that those numbers don't line up. Even if you're willing to live more frugally than the typical senior, you'll still need more than your Social Security benefits to maintain a decent standard of living, and that's where personal savings come in. The money you accrue in your 401(k) or IRA could spell the difference between struggling financially in retirement and paying your bills with relative ease.

There's just one problem: An estimated 10% of Americans don't have any money set aside for retirement, according to a recent Transamerica survey. And those who don't take steps to start saving may be in for a world of financial hurt later in life.

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If you don't have any money in a dedicated retirement plan, it's imperative you make savings an instant priority. Here's how to build a nest egg that serves you well during your senior years -- even if you're starting with nothing.

1. Begin living more frugally 

Chances are, there are some expenses in your budget you can cut without it having too great an impact on your quality of life. Comb through your bills and identify a few you can cut back on initially. That could mean ordering food delivery less frequently or canceling the gym membership you don't use that often anyway.

2. Start small and work your way up

Currently, you can contribute up to $6,000 a year to an IRA if you're under 50 or up to $7,000 if you're 50 or older. With a 401(k), these limits are much higher -- $19,500 for workers under 50 and $26,000 for the 50-and-over set. But if you're not in the habit of funding a retirement plan at all, you can't be expected to magically start maxing one out overnight.

What you can do, however, is start contributing $50 here or $100 there to your retirement plan and increase your savings rate over time. You might, for example, only manage to save $300 in total this year, but then pledge to save your entire $2,500 raise in 2021 and every other raise from that point forward.

3. Invest aggressively to boost your savings

The money in your retirement plan shouldn't just sit there in cash (though if you're very close to retiring, a small portion should). Rather, invest your savings to grow that money into an even larger sum over time, and the best way to do so is to focus on stocks. Though they're more volatile than bonds, when you're dealing with a lengthy savings window, you have plenty of time to ride out market downturns and come out ahead. On the other hand, if you stick with conservative investments, like bonds, you may wind up disappointed with your total savings balance.

Imagine you start setting aside $200 a month in a retirement plan at age 37, with the goal of retiring at 67. If you play it safe and invest heavily in bonds so that your account generates an average annual 4% return, you'll end up with about $134,600 after 30 years. But if you go heavy on stocks so that your retirement plan delivers an average annual 7% return instead, you'll grow your savings balance to about $226,700. That's a $92,000 difference, all for contributing the same amount of money over time.

Even if you don't plan to live it up in retirement, you'll still need money beyond what Social Security will pay you. Do your best to build up a sizable 401(k) or IRA balance while you can. You'll be grateful for that extra income once you realize just how costly your senior years actually are.