Issue 049 - Federal budget - Interest-cost scaling
What does $40 trillion of U.S. debt cost each year?
U.S. federal debt has surpassed $40 trillion, renewing debate over deficits, taxes, spending, Treasury yields, and the rising cost of government borrowing.
The problem
Estimate approximately how much interest the federal government must pay each year on $40 trillion of debt.
Then convert that annual interest burden into an equivalent cost per U.S. household per year.
You'll need to estimate the effective average interest rate being paid across outstanding government debt, the number of U.S. households, and whether all $40 trillion should be treated alike for this estimate.
As a second comparison, consider whether the annual interest bill is closer in scale to a major federal program, the defense budget, or total discretionary federal spending.
Because Fermi problems target an order of magnitude, I normally use no more than two significant digits and write most calculations in scientific notation; the Fermi reference explains both conventions.
Before checking sources
Matt's first pass
I assumed that when we talk about federal debt, we are talking primarily about bonds. Bond yields can fluctuate, but I think I have seen numbers ranging from 1% to 4%, so I treated the entire debt as uniform and used an average yield of about 1.5%.
federal debt ~= $40 trillion
~= $4 x 10^13
average interest rate ~= 1.5%
~= 1.5 x 10^-2
annual debt service ~= $4 x 10^13 x 1.5 x 10^-2
~= $6 x 10^11/yearNext, I assumed about 330 million Americans and about 2.5 people per household, which gives about 130 million households.
households ~= 3.3 x 10^8 people / 2.5 people/household
~= 1.3 x 10^8 households
cost per household ~= $6 x 10^11 / 1.3 x 10^8
~= $4.6 x 10^3/household/yearThat gives an annual debt-service cost of about $600 billion, or about $4,600 per U.S. household per year.
Calibration Score
Matt's Calibration Score: 70 / 100
Higher is better: earn points for accurate pegs, sound models, correct math, and a result close to the sourced answer. The image shows percent full of it: 100 minus the Calibration Score.
Pegs: 10/30. The household peg was solid, but the effective interest-rate peg was low enough to move the answer by roughly a factor of two.
Model: 30/30. Debt times effective rate, then divided by households, is the right first-order model.
Math: 10/10. The arithmetic was clean given the assumptions.
Result: 20/30. The final per-household estimate was low but still comfortably within one order of magnitude of the sourced check.
Grounding facts
Reuters reported that U.S. federal debt topped $40 trillion as borrowing costs and Treasury yields drew renewed attention.
CBO projected that net federal interest outlays would rise from about $970 billion in 2025 to a little over $1.0 trillion in 2026.
Treasury's average-interest-rate data show many marketable Treasury categories in the 3% to 4% range in mid-2026, while the 10-year Treasury yield was about 4.8% on September 2, 2026. New market yields are not the same as the average rate on all existing debt, because older debt rolls over gradually.
A useful household peg is still about 1.3 x 10^8 U.S. households. Also remember that gross federal debt, debt held by the public, and CBO's net-interest measure are related but not identical.
After checking sources
Check and recalibrate
The simple gross-debt calculation is a good way to see the scale. If the effective interest rate were about 3%, the carrying cost would be:
gross debt ~= $4 x 10^13
effective rate ~= 3 x 10^-2
gross interest ~= $4 x 10^13 x 3 x 10^-2
~= $1.2 x 10^12/yearThat is about $1.2 trillion per year. But the cleaner budget comparison is CBO's net-interest outlay estimate, which subtracts federal interest receipts and reflects the actual budget line.
CBO net interest ~= $1.0 x 10^12/year
U.S. households ~= 1.3 x 10^8
net interest per household
~= $1.0 x 10^12 / 1.3 x 10^8
~= $7.7 x 10^3/household/yearSo the best scale answer is around $8,000 per U.S. household per year using net interest, with a simple gross-debt model plausibly landing closer to $10,000 per household per year.
That puts the annual interest burden in the thousands of dollars per household, not hundreds and not tens of thousands. As a federal-budget comparison, a trillion-dollar interest bill is in the same broad neighborhood as defense-budget scale and roughly half of CBO's projected total discretionary outlays of about $1.9 trillion in 2026.
Post-check reflection
Matt's reflection
Looks like my interest-rate estimate was less than half the more realistic current-rate number. That means my final estimate was about half what it should have been, but in the world of Fermi estimates, that is not wildly off.
While this is a huge number, it is not unimaginable in terms of the earning capacity of each household. If the average household earns something like $50,000 to $60,000 in the U.S., then a burden under 20% of that earning capacity is a big chunk, but manageable. Still, that is big.
Recommended memory peg
For federal-debt problems, remember: 1% of $1 trillion is $10 billion, so 1% of $40 trillion is $400 billion. A federal net-interest bill around $1 trillion/year is roughly $8,000 per U.S. household per year.
Reader results
Bars show how submitted estimates sort into the answer choices from the gut-check prompt.