A little pain now can make you feel better later. Photographer: Luke Sharrett/Bloomberg

A few weeks back, when I wrote about the joys of the 15-year mortgage, I got the same reaction from a lot of people: “Why would you repay a loan when at these low rates, it’s practically free money?”

I hear this about a lot of things. “Why would you buy a car for cash/save up to remodel the kitchen/have an emergency fund instead of a home-equity line of credit? Mathematically, that’s insane!”

I don’t think it’s quite as arithmetically unreasonable as my interlocutors suggest. Once you add risk into the equation, the calculations don’t come out quite so neatly. By refinancing to a 15-year mortgage with a lower rate, we locked in 125 basis points a year, completely risk-free. And when the mortgage is completely paid off, we’ll get another 3.25 percent, 100 percent guaranteed and risk-free. There are no risk-free investments that deliver that kind of return. You can make more money by adding risk -- but you can lose more that way, too.

Moreover, math is not the only consideration. As I’ve noted before, personal finance is not primarily about math; the arithmetic part is so easy that even journalists can do it. The hard part is discipline.

From time to time, I write about Dave Ramsey, the personal-finance guru who advises people to get themselves entirely out of debt. A lot of people think that the power of his program is getting rid of all those interest payments. And if you have a huge mountain of 18 percent credit card debt or you’re cycling thousands of dollars' worth of payday loans, then yeah, the interest rate is your big problem.

But for most people, that’s not the case. For most people who are really struggling with debt, the principal is their problem, not the interest: the \$30,000 truck on a \$35,000 income, the six-figure student loans, the house in the “stretch” neighborhood that’s eating up 40 to 50 percent of every paycheck. Going debt-free fixes their problem not by saving them all those interest payments, but by making it harder to buy things they can’t afford.

Every purchase is a trade-off; you buy this, thereby giving up the opportunity to buy that instead. Debt makes those trade-offs less painful because people care more about now than later. So you get to have this right now while leaving most of the foregone consumption for later periods. Effectively, you lower the current emotional price of consuming something expensive.

Unfortunately, you don’t lower the total emotional price. Later, those trade-offs may still have to be made, and because you had imperfect information, they may turn out to be painful indeed -- that extra \$250 a month on the mortgage may be the price of the travel soccer team your child is dying to join or flying across the country to see a sick relative.

So aside from risk, one major reason to buy on cash rather than credit is to make the sacrifices first, so that by the time you buy, you know exactly what you’re trading off to get the object of your desire -- and that those trade-offs are worth it to you.

Not everyone needs to do this, of course; some people are good at handling credit, while some people can’t control themselves. Long before we decided to refinance to a 15-year mortgage, we decided to take out much less mortgage than we could afford in order to give us more breathing room in our budget; if we hadn’t been disciplined enough to do the latter, then we wouldn’t have been in a position to move to a shorter-term loan.

But even if you’re relatively disciplined, you might be surprised to find how much further a little extra discipline can get you. When I wrote about the Ramsey plan for the Atlantic in 2009, I actually tried his all-cash plan, and I was shocked to find out how much money I saved. Our budget wasn’t particularly extravagant before, and I’d allocated cash into the various envelopes based on what we were already spending. But somehow having to spend cash out of an envelope rather than just pulling out the debit card made me much more frugal. I’d been terrified of running out of money, but we finished the month with extra cash in every single category.

That’s the power of making your trade-offs explicit. And that’s why we’re now trying to save up front for things that other people -- even thrifty people with sterling middle-class values -- would finance.

To contact the writer of this article: Megan McArdle at mmcardle3@bloomberg.net.

To contact the editor responsible for this article: Brooke Sample at bsample1@bloomberg.net.