How many of you would turn down $1,000 if I offered it to you, no strings attached? $5,000? I thought so.

But when it comes to financial matters that are more complex than greenbacks in the hand, even the best of us can be swayed by the gut. Take the age-old dilemma facing Americans: Should I pay down debt or invest?

My wife's a payer. She prefers the peace of mind that comes from having low debt. I like that too, but I'm an investor. If I think I can earn more on a lump of money than I could save by using it to pay back a debt early, I'd rather invest. After all, exploiting the "spread" between the borrowing rate and the lending rate is how banks like Citigroup (NYSE:C), Motley Fool Income Investor pick J.P. Morgan Chase (NYSE:JPM), and Bank of America (NYSE:BAC) make billions.

Granted, investing money that could be used to pay down debt isn't always the easiest decision, since stock investing comes with risk that's missing from simple repayment. If your shares have negative returns over the life of the loan, like, say, our good friendXerox (NYSE:XRX) or Eastman Kodak (NYSE:EK) have shown over the past decade, then you'd have been better off paying back the loan. Even boring dividend stuff isn't risk-free. If GM (NASDAQ:GM) keeps reducing sales at a 25% clip, that juicy-looking 7% yield isn't going to be worth much, if it lasts at all.

Luckily, I recently came across a no-brainer in our home finances, and others may find themselves in the same position. As interest rates have begun to creep up, it happens that there are now risk-free yields -- CDs, money market accounts, and savings accounts -- that exceed the rate we're paying on an old student loan.

That means it no longer makes any sense at all to pay back that loan early. We can make more on the money earmarked for repayment than we would save by early repayment.

Here are some hypothetical numbers -- streamlined and ignoring tax issues for simplicity -- that mirror reality. Assume a $20,000 loan over 10 years, with payback starting today, at an interest rate of 3.6%. (I know people with loans at even lower rates.) Now, with a little bit of work, you can find a savings account out there that that pays 3.35% to 3.93%. Let's take the high end of each.

The table below summarizes the interest "saved" by paying down the 3.6% loan early, via three methods: paying an extra $100 per month, an extra $200 per month, or paying the entire $20,000 up front.

Hypothetical excess payment

Total interest paid

Interest "saved" over original payment

$0 extra

$3,845.20

$0

$100 / month

$2,359.49

$1,485.71

$200 / month

$1,707.86

$2,137.34

$20,000 up front

$0

$3,845.20


Looks like a lot of money, right? It is, but it pales in comparison to the amount you could earn by taking the excess debt payment and investing it at the higher rate over the same period.

This table summarizes the interest you could earn on that money if you put it into the aforementioned 3.93% savings account over 10 years. The second column shows the amount of money you lose by paying off the loan early. (Hypothetical interest earned on savings, less hypothetical interest "saved" by early repayment.)

Hypothetical excess payment

Interest earned at savings account

Interest "saved" by early debt payment

Amount lost by paying early

$100 / month

$2,670.76

$1,485.71

$1,185.05

$200 / month

$5,341.52

$2,137.34

$3,204.18

$20,000 up front

$9,609.35

$3,845.20

$5,764.15


While the amounts here aren't huge, they're compelling enough to overcome the gut feeling that repaying the loan early is somehow the more "responsible" thing to do. If you carry student loans, take a look at the math and see what makes sense. There are few opportunities in life to earn free money with no risk. Take them every time they come along.

Related Foolishness:

  • For more info on savings, checking, CDs, and other basics, visit our Savings Center.
  • A constant stream of income is one way to be wrong and get rich anyway.
  • Want to find the easy money? Learn the secrets of free cash flow.

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Seth Jayson will gladly take free money any time you wish to send it. At the time of publication, he had positions in no company mentioned here. View his stock holdings and Fool profile here . Fool rules are here .