So big gummint is spending big bucks.
They have revenues of three trillion dollars. Expenses are three and a half trillion dollars. (Fairly clean numbers last year.) Somehow they spent more than they took in. How did they do that? Couple different possibilities.
1) They could have printed up the money they were short. 2) They could have borrowed the money they were short.
We're not maneuvering wheelbarrows full of Benjamins through the streets in order to pay ten billion for a cuppa at Starbucks, so it's already pretty clear which option Treasury chooses to finance the deficit. But it's still interesting how they manage this whole thing.
They have an auction. Plain old auction.
Big banks and insurances companies and pension funds and mutual funds and international governments have cash. They have lots and lots of Bennies. Treasury needs cash. They don't go to the Fed to ask them to print new money to pay for government spending because that would be a dumb Weimar/Zimbabwe/wheelbarrow thing to do. Treasury goes to the markets, to all those banks and governments and other money folks, and they try to borrow the cash that's already out there in the world, cash already printed up earlier for reasons entirely unrelated to the federal budget. (I'm using "print" loosely here. Most of this stuff is digits on computers.)
So Treasury says, "Hey, I'm selling a thousand dollar bond! It matures in one year! Who wants to buy this shiny thousand dollar bond!"
Of course, it's all soh-fist-tuh-kated but I like to imagine a quaint movie auction. The over-dressed clients are sitting in their uncomfortable chairs, and they're bidding on the chance to receive one thousand bucks one year from now. "I'll pay 900 bucks for 1000 a year from now!" the first rich person says. "I'll pay 950!" "I'll buy 975!" Then the mysterious stranger in the back speaks up. "I'll pay 990 dollars and 10 cents today to receive 1000 a year from now."
"Sold!" Treasury says, "to the mysterious stranger in the back!"
Treasury receives 990.10 today, and they have an obligation to pay 1000 to the mysterious stranger after one year. With a little algebra we can see that they will be paying back 9.90 more than they're borrowing, and as it happens, 9.90 is one percent of how much they borrowed.
The rate is 1% on this hypothetical bond. This is how the "interest rate" is discovered.
That's a hypothetical. What about rates right now? If the auction were held today, how high would it go? Higher than 990.10 for a certainty. "991!" bids a bank. "995!" bids another. "997!" "998!" Then a baritone voice cuts across the room. "998.30!" says the mysterious stranger.
A 1-year US Treasury -- the name of the government department is also the name of the debt obligation -- would sell today at about 0.17% interest. That is the expected rate. There's no auction today. (At least, I don't think so. I don't keep track.) But there was an auction on 1-year Treasuries not long ago. That money is due in 11 months. And there are older Treasuries out there in the world, maybe 2-year or 5-year or 10-year when they were first issued, but they've been out in the world a long time and they come due in 13-months or so. So basically, they are equivalent to 13-month Treasuries, and they're circling the markets even as we speak, being bought and sold as banks and insurances companies and all the rest wheel and deal on the secondary market. The primary market comes from Treasury, and only Treasury, at set intervals for the auctions, but the secondary market is always alive and always trading.
We can estimate what the price of a 1-year Treasury would look like by finding the price of the bond that matures in just a little less than a year, and finding a bond that matures in just a little more than a year, and splitting the difference of their rates. Sometimes firms use complicated formulas for this, but the basic idea is simple. We just look at the prices on the secondary market, and do a little calculation.
(The secondary market is also extremely important for stocks. Companies don't sell shares of ownership every day. A primary market transaction like an IPO doesn't happen all that often. Almost all the news you hear about the stock market going up and down is the secondary market, as people entirely unrelated to the company sell shares back and forth. A robust secondary market makes it much easier for the primary market to work well, whenever a company wants to sell more shares. Since people are trading older shares back and forth all the time, it's dead simple for the company itself to throw some new shares into the mix in order to raise funds.)
Obviously, the higher the price of the bond, the lower the interest rate. If the government is selling a thousand dollar bond, payable in one year, and the buyers bid up the price to one thousand dollars, then the interest is zippo. During the financial crisis, this actually happened. There were auctions where people would pay slightly more than a 1000 to receive 1000. They received negative interest. They didn't believe they could store the cash anywhere safe. The government basically took a "fee" to keep the money secure, like renting a safe deposit box.
When countries are selling one-year 1000 euro bonds, and the auction bids up the price to 900 euros, then the country is paying more than 11% interest. Inflation is low in the eurozone. Such a country has very serious problems.
APPENDIX: YIELD VERSUS COUPON
There is one more complication that might not be strictly necessary to address, but it's an important characteristic of bonds as they actually work in the real world. I'd feel negligent not bringing it up.
It would be very easy for Treasury to sell 10-year bonds in the same way they sell 1-year bonds. They could make the offer, "Who wants to buy the chance to receive 1000 ten years from now?" A one percent annual rate (compounded annually) would mean the auction-winning price would be 905.30 today. They could totally do this.
They don't do this.
Instead, the longer-term Treasuries come with "coupon" interest payments. In ye olden days, this was a literal coupon that could be detached from the paper bond and submitted for the interest payment. A bond with a thousand dollar face value and a 1% coupon will make two semi annual payments of five dollars. (Two coupon payments a year means 10 dollars, which one percent of the face value of the bond. The bond pays 1% in coupon interest yearly.)
This is the bond that is put on auction. Treasury goes to the money people. "Money People!" Treasury says. "We're selling a 1000 dollar bond (face value) with 1% coupon. Who wants some of this? Who wants some? YOU WANT SOME OF THIS? DO YOU????"
And the auction proceeds normally from there.
Although the face value of the bond is one thousand, that is not the market price of the bond. The face value is important because coupon payments are based on the face value, and the bond will return the face value when it matures, but at the actual auction, people might pay more or less than the face value based on what kind of safety they want and what kind of return they might expect from other places in the economy. In business contexts, "100" is often used as the standard face value (as in 100%) and current bond prices are given as some number above or below 100.
This is how the yield is technically different from the "interest rate" (the coupon interest rate) of the bond. The yield is much more important.
The bond might have a face value of 1000 dollars, but it can still sell at 990 dollars. The coupon payments are the same, but the purchaser bought the bond for less than face value, so their yield is actually higher than the stated coupon interest rate. They're receiving 1% of 1000 annually, but maybe they only paid 900 dollars for it. If the price of the bond exceeds 1000 dollars, then the actual yield is lower than the stated coupon interest rate.
In the vast majority of cases, nobody gives much of a crap about the coupon interest rate. It is the yield which is all important.
When I'm talking about rates on bonds, I am essentially always talking about the yield.