There’s no right answer here precisely because circumstances are unique for every family, but also for each future.

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Police officers have been known to say that the last thing they want to get involved in is a domestic dispute.

The same can be said for personal-finance columnists.

There’s no hiding that money can be the root of many problems within relationships and marriages, so when the children of neighbors saw me walking the other day and the young husband hoped I would “settle an argument” they were having, my nerves started jangling.

Ultimately, however, I wound up in the middle of a common situation, with an answer that left Jeff and Kristen arguing, because — as with most things in personal finance — there is no one “right” answer, even though most people think there is a clear-cut response.

Here’s the back story: Jeff and Kristen got married a few years back, and now have one child. They have been financially frugal and avoided debt; before their marriage — and then as a newlywed — she had always maintained an emergency fund.

With the birth of their son, however, they had a few unexpected expenses and racked up credit-card debt for the first time as a couple (Jeff had some previous debt that he had paid off before they married.)

Now they have roughly $5,000 in card debt racking up interest at a double-digit rate, and $2,500 sitting in the emergency fund, earning virtually nothing.

Jeff wants to use that money to pay down debt, figuring they can fall back on the plastic in any emergency. Kristen doesn’t want to crack the rainy-day fund until she’s damp.

Jeff is trying to minimize the debt. “If we pay off the debt faster, we can rebuild the emergency fund faster,” he said.

Kristen countered with a great line: “Credit-card debt isn’t a real emergency.”

Both have a point.

A Federal Reserve survey last year estimated that nearly half of all American households could not handle an emergency expense of just $400. In January, the latest Financial Security Index from BankRate.com showed that more than one-third of households (34 percent) endured a major unexpected expense in the previous year; just under 40 percent of the survey respondents said they had the savings to cover a $1,000 shock.

Moreover, when calamities did happen, the average expense was more than likely going to cost at least $2,500. That’s precisely why Kristen sought a high-yield online savings account and built the rainy-day fund; it’s not earning much, but it’s building her peace of mind.

Jeff is confident in his job and the couple’s prospects. He noted that they have solid investments, have not really struggled with moving into a new home and starting a family. They could liquidate some assets — or shut off contributions to a retirement plan — to pay off the debt, “but I am making as much or more money in the stock market than I am paying in interest charges on the cards, so the place where it makes sense to change things is with the emergency fund, because it’s not earning much.”

There’s no right answer here precisely because circumstances are unique for every family, but also for each future. Tapping the emergency fund is a great idea from a financial-efficiency standpoint, provided it isn’t actually needed before it is replenished; it’s a mistake if there is some emergency that puts the couple deeper in debt before they can refill the emergency tank.

That is precisely why researchers from the Federal Reserve Bank of St. Louis looked at this phenomenon and concluded that having cash on hand is crucial for avoiding financial hardship.

The results were not a big surprise: having cash or other assets predicted lower risk of encountering any kind of financial hardship, from missing payment on rent, a mortgage or a recurring bill to being forced to skip necessary medical care and more. Having debts increased the risk of hardship.

But in using research to predict outcomes, the researchers found that having cash on hand predicted a significantly lower risk of every type of financial hardship they looked at.

Without getting lost in the mathematics of the formulas, a $100 increase in savings would reduce the probability of a household falling into rent or mortgage delinquency by 4.6 percentage points.

“This effect is sizable,” wrote authors Emily Gallagher and Jorge Sabat, “considering the probability of falling into rent or mortgage delinquency within six months was 4.5 percent.”

The impact of $100 in extra cash on hand was even bigger in the other hardship categories the researchers looked at.

By comparison, increasing high-interest debt made less difference in the likelihood of falling into a sudden hardship, which makes sense because the households that have access to credit can use it to sidestep trouble, even if it is an expensive way to power through problems.

Ultimately, Gallagher and Sabat concluded that holding a small buffer of cash for emergencies is better than paying down high-interest debt for the stability of the household.

So while Jeff’s thinking about paying down the debt made sense, the truth is that the unexpected costs were not a true financial shock, thus they really shouldn’t qualify as something worthy of the emergency fund. Moreover, tapping the disaster funds would be unsettling to Kristen’s peace of mind about the family finances, at least until the savings is restored.

That’s precisely why personal finance isn’t always black-and-white. I could argue both sides of this argument with equal conviction. Kristen felt vindicated by the discussion, but Jeff was unchanged in thinking, correctly, that the math would be most favorable if he reduced the debt and then rebuilt the savings.

Ultimately, however, the “right” call in these situations depends on someone’s dedication to completing the tasks — actually paying off the debt/rebuilding the savings rather than letting other situations get in the way — along with personal circumstances and maybe a bit of luck in avoiding common troubles. In all cases, agreeing to a course of action and seeing it through will deliver the best results in the end.