If you're a new parent, you're probably spending your days adjusting to life with an infant and figuring out ways to work showers and sleep into your new, exhausting schedule. But before you fill up your downtime -- if we even want to call it that -- with household chores and the like, you may want to carve out some time to develop a college savings plan for your child.

If you're thinking it's too soon to start worrying about college when you're currently charging diapers on a credit card, here's some sobering news: In 2036, the average cost of college at a four-year private university will reach $303,000. That's up from an already whopping $167,000 at present, according to projections from investment platform Wealthfront.

Willing to slum it at a four-year public university? That'll run you about $184,000 in 18 years compared to just $101,000 today -- "just" being a relative term, of course.

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When you look at these numbers, your first inclination might be to throw your hands up in the air and resign yourself to the fact that you're never going to make a dent in your child's education. But before you give up hope, remember that if you save wisely and aggressively for college, there's a good chance you'll cover more of those costs than you think.

Saving efficiently for college

If the idea of saving anywhere close to $303,000, or even $184,000, seems daunting, remember that if you start setting aside money the moment your child is born, you'll be giving yourself a pretty decent window to build a nice college fund. The key, however, is to invest that money efficiently, and that's where 529 plans come into play.

Here's how these plans work: You put money into an account and invest it just as you would with an IRA or 401(k). Though you don't get an immediate federal tax break for funding a 529, your money gets to grow tax-free and withdrawals are yours free and clear of taxes, provided you use that cash for education purposes. (It used to be that those funds were earmarked for higher education only, but recent changes to the tax code now allow you to use your money for private grade-school education, as well.)

This means that if you invest $40,000 of your own money in a 529, and that balance grows to $80,000 by the time your child is ready for college, that additional $40,000 is yours to use without having to worry about the IRS coming in and nabbing its share. Furthermore, some states give residents a tax break for participating in their plans, and a few states offer a tax break for contributing to any 529.

If there's one drawback to saving in a 529, it's that if you overfund your account, you could face a 10% penalty on funds you withdraw for non-education purposes. However, that penalty applies to the gains portion of your account only -- not your principal.

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So how much might you manage to save for college if you start early enough? Let's assume you're able to set aside $500 a month over an 18-year period. If your investments generate an average annual 7% return during that time, you'll wind up with roughly $204,000 -- enough to fund a four-year public education. Make it $750 a month and you stand to accumulate $306,000, which will cover a private college education as per the aforementioned projections.

Of course, setting aside $750 a month or even $500 a month is easier said than done, but if education is important to you and you'd like to minimize the extent to which your child racks up student debt, you have a real opportunity to amass some nice savings, provided you start early enough. And if you save that money in a 529 as opposed to a traditional brokerage account, you'll get the benefit of tax-free gains to help boost that education fund.

A 529 isn't your only tax-efficient savings option. You can also save for college in a Roth IRA where you'll enjoy the same tax-free growth as a 529. The only problem is that Roth IRAs currently max out at $5,500 a year for savers under 50 and $6,500 for those 50 and over. There's a good chance these limits will increase over time, but if they don't, it means that if you start saving for college at age 30 and continue doing so until age 48 -- even if you max out your Roth and choose investments that deliver a 7% average annual return -- you'll only be looking at $187,000. While that is enough to fund a public four-year degree 18 years from now, it's nowhere close to covering a four-year private education.

Furthermore, higher earners aren't eligible to fund Roth IRAs directly. And since those with robust incomes are the most likely to have the means to save consistently for college, that's a nod in favor of 529s.

Ultimately, no matter where you house your college fund, the key is to choose a tax-advantaged plan and give yourself the lengthiest savings window possible. So do that -- and then cross your fingers and hope that the college bubble bursts like crazy between now and 2036.

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