In some families, teenagers contribute to basic costs like housing. In others, parents expect summer earnings to replace a weekly allowance. Many teenagers save for their first car, and few among the college-bound escape the pressure to put money away for tuition.

Some parents dictate the terms, while in other families, there's a negotiation over how to divide the money once a summer job has ended. It's rare, however, that families consider the possibility of giving a child a running start on retirement savings.

It's a shame, too. That's because the boost that comes from opening a retirement savings account as a teenager instead of a few years after college can lead to hundreds of thousands of extra dollars after a half-century of growth.

Most of us have seen basic compound interest graphs before, so we know how the math works for grown-ups who start setting money aside from their first full-time paycheck. But beginning even earlier supercharges the savings for families that can afford it — or who reel in grandparents and others willing to match a child's contributions.

The process starts with a Roth individual retirement account, and it will need to be a custodial account, with an adult cosigning, if the teenager is under 18. The nice thing about Roths is that you generally pay no taxes on the withdrawals. So the money will grow for many decades and then come out tax-free as long as the rules don't change. While there are no tax deductions for deposits, that doesn't mean much to teenagers whose income is so low that they may not pay any income taxes at all.

If you're trying to persuade children or grandchildren to save rather than ordering them to do so, you could start with some simple numbers. If you take $5,000 in savings from a few summer jobs and put it in a Roth at age 19, it will grow to $52,006 by the time you're 67 if it grows at a 5 percent annual rate. Wait until 25 to start with that same $5,000, however, and the balance at age 67 is just $38,808. You can plug your own numbers and investment return assumptions into the Roth IRA calculator at dinkytown.net.

Things get more interesting, however, if you pledge that once a Roth is open, you'll spend a few years helping a young adult max out the $5,500 contribution each year as long as that person earns the $5,500 necessary to make a deposit of that size. If that 19-year-old starts with $5,000 and makes the maximum contribution each year until 67, the ending balance is $1,164,985 if it grows at a 5 percent annual clip. That's over $330,000 more than what someone would end up with if they waited just six years, until age 25, to start the Roth and then saved the same amount.

For grandparents, uncles, aunts and others looking for a way to make a meaningful contribution to a child's future financial stability, this is a nice way to do it while directly rewarding hard work. You might match some or all of what teenagers make and even open the account with them. It's also fine for you to give them the matching funds for the Roth, while all of their actual earnings go toward the car, college or allowance replacement.

Some families do seem to be catching on to these possibilities. At Charles Schwab, 87 percent of all custodial accounts are Roths.

Parents may worry about the financial aid implications, given that colleges generally want families to turn over a large chunk of student assets each year. The good news here is that when you're filling out the FAFSA form to determine eligibility for various forms of federal financial aid, a student's Roth or other retirement account is not part of the calculation.

Scores of colleges and universities do require families to fill out an additional form known as the CSS/Financial Aid Profile. On it, student applicants must report a single total for all their retirement balances as of the end of the previous year. In theory, these schools could take this number into account when determining how much of their own grant money to award the applicant.

But for now, few, if any, colleges appear to be penalizing students for owning a Roth. Eileen O'Leary, assistant vice president for student financial assistance at Stonehill College in Easton, Mass., said she had seen a financial aid applicant disclose a retirement account only once. Kal Chany, who advises families through his firm Campus Consultants in New York City, has had only a handful of college applicants as clients who also had retirement accounts. Even though some of them have had balances upward of $10,000, he knows of no adverse impact on financial aid so far. Still, he said he feared that might change if lots of families started putting their children's earnings in Roths or matched those earnings with their own money.

For now, however, the risk seems reasonably small for families applying for financial aid. The potential gain over many decades for all families is enormous, especially if the supervision turns the young adult into a regular saver who maxes out the contributions early in life and continues to do so.