HOW can governments borrow most cheaply? The answer matters hugely for taxpayers. Take America: it has $14trn in outstanding national debt, fully three-quarters of GDP. Interest payments alone are expected to reach $280bn this fiscal year—ie, more than three times the combined budgets of the Departments of Education, Labour and Commerce.

The problem largely comes down to deciding how much long, medium and short-dated debt to sell. Almost every country issues a combination of these maturities. In the current low interest-rate environment, however, many argue that governments should sell proportionately more long-dated bonds to make sure they are able to pay historically low rates for many decades to come, thereby saving taxpayers money in the long run.

Some countries have already ploughed ahead. In recent years Britain, Canada and Italy have sold 50-year bonds; Mexico, Belgium and Ireland have issued 100-year debt. The latest country to flirt with the idea is America: last month the Treasury sent out a survey to bond-dealers to gauge market appetite for 40-, 50- and 100-year bonds. On May 3rd officials said that Steve Mnuchin, the treasury secretary, had set up an internal working group to take a look at ultra-long bonds. Mr Mnuchin has expressed the view that they could “absolutely” make sense.

Not everyone agrees, including, it seems, the private-sector financiers who make up the Treasury’s own borrowing advisory committee, which met this week. Long-term rates are at historic lows but short-term rates are even lower. The weighted average maturity (WAM) of outstanding Treasury debt is 5.7 years, and the effective interest rate paid on the total pile of debt is 2.03%. The yield on 30-year Treasuries is 3%, so selling even longer-dated debt will raise the overall cost. Even a 0.1 percentage-point rise would add roughly $14bn to the taxpayer’s burden.

Moreover, ultra-long bonds would be cost-effective in the long run only if short- and medium-term interest rates eventually exceed the levels of long-term rates today. Otherwise governments could simply roll over short-term debt. Issuing very long-term debt is, in effect, like paying for insurance against future interest-rate rises.

So whether ultra-long bonds would save taxpayers money depends on future inflation and growth. Higher levels of each would probably push up short- and medium-term interest rates. But this is not inevitable. Alex Gurevich of HonTe Investments, a California-based fund-management firm, says interest rates in America are more likely to remain at current levels than to revert to the mean seen in the late 20th century. If Mr Gurevich is right, ultra-long bonds sold today may, ironically, lock in higher rates for longer.

Finally, the demand for ultra-long government bonds is unpredictable. Institutional investors with long-term liabilities, such as pension funds and insurance companies, may be happy with 30-year bonds, which most countries already sell, or may opt for higher-yielding long-dated corporate bonds, such as those issued by Caterpillar, an American construction-equipment company. Sales of ultra-long government bonds, despite fanfare, have so far been one-off events and do not provide much of a guide. Low demand would in turn send yields higher, raising government debt-servicing costs.

In some countries, such as Britain, interest rates on long-term debt are not much higher—or are even lower—than on shorter-term borrowing. For them, borrowing at ultra-long maturities is likely to be cheaper than medium-term debt, so it makes sense to replace some mid-length bonds with ultra-long ones, says Niso Abuaf of Samuel A. Ramirez & Company, a New York brokerage. This helps to explain why the WAM of British sovereign debt is unusually long, at 14.9 years (see chart).

Ultra-long debt is also very attractive to governments such as Mexico’s, which have a recent history of fiscal profligacy and high inflation, yet are able, while investors still trust them, to borrow for the long term very cheaply. In America, however, where Treasury bonds serve not just to raise funds but to set global benchmarks, the calculation is a trickier one.