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What should take priority: saving for college, or retirement? 

Sometimes, the greatest harm parents can inflict occurs with the best of intentions.

In the world of finance, nowhere is that becoming more evident than in the heart-wrenching decision of whether to save for one's retirement, or put money toward a child's college education. Of course, in a perfect world, you would be able to do both, but for many Americans, that simply isn't possible.

When you look at the headline numbers, the choice to pay for your child's education seems obvious. Those who earn their bachelor's earn far more and have lower rates of unemployment, and helping your student avoid the heavy burden of student loans makes sense.

Throw in there the fact that they are your child, and a great many parents make the choice to funnel their extra cash toward tuition instead of retirement.

But a recent survey by TD Ameritrade reveals how making this choice could boomerang and hurt not only yourself, but your child's future finances.

Surprising results
The popular narrative we see in the media now is that millennials are having a tough time getting ahead because of crushing student debt and a lousy job market. As a result, as many as 36% are living at home with mom and dad.

The reality is that the student debt problem is largely the result of a boom in for-profit college debt, and that those with a college degree are finding jobs. Also, those numbers on millennials living with their parents count college students, which doesn't seem fair at all. Of those over the age of 25, only 16% are living at home.

But TD Ameritrade's study, which aimed to find out how much financial support family members provide to their adult kin, revealed a surprising result. Overall, one-fifth of Americans are providing some type of substantial financial support to another family member. This primarily comes from parents providing for adult children, and adult children providing for elderly parents.

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Source: TD Ameritrade.

But while the overall percentage of Boomers who are "Financial Supporters" eclipses the percentage of millennials who find themselves in that role, the actual amount of assistance provided is skewed in a major way -- and in a direction you wouldn't expect.

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Source: TD Ameritrade. arrows and annotation added by author.

This is astounding. While a Boomer is providing roughly $9,700 per year, mostly for adult children, the average millennial is providing almost twice that amount to help their parents cover living costs.

Think about that for a second.

While college costs normally accrue over four or five years, possibly running between $75,000 and $100,000 at public institutions, the assistance being provided by millennials continues for an indeterminate amount of time -- and at a very high level.

In the end, there is one huge mathematical problem with paying for tuition over saving for retirement. Every dollar you put toward college savings (or directly toward tuition) doesn't get a chance to grow in your retirement fund. Therefore, that money is missing out on the most powerful weapon you have at your disposal: compound interest.

Consider: If you are 45 and contribute $10,000 to your child's tuition, that money immediately disappears. If you invested that $10,000 between now and when you retire at 67, that money -- assuming normal market returns of 6.9% after inflation -- would have grown to roughly $43,000 in today's dollars.

Taken from this perspective, it's not a $10,000 tuition check you're signing, but also a $43,000 withdrawal from your retirement account. Do this for four or five years, and for multiple children, and you'll see how you're not just paying for tuition -- you're largely throwing your retirement away.

The sad irony is that when retirement time comes, it will likely be your children -- those who you intended to help in the first place -- who will bear the brunt of your shortfall. It's tough to tell a child that they have to pay their way to college, but if it's a choice between that or retirement, the data is clear.

Remember, there are ways for non-rich people to graduate from college without crushing debt. But there's no way to get those years of compounding retirement savings back. In the end, being a little selfish ends up working out best for everyone.

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