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So first of all, don’t forget the Federal Reserve has also lowered the Federal Funds Rate. And remember they do this by basically increasing the money supply. Here’s a good video…
Now, the whole issue is, generally when money is borrowed, there are terms on which the contract is made…terms which among other things lay out the payment schedule, which will dictate how the loan is repayed.
When a loan is repayed in periodic payments consisting of principle and interest (as most loans are), these periodic payments are referred to as “debt service”. The borrower is said to be “servicing the debt” with these payments. The amount of each payment is usually a function of the amount borrowed, the length of the loan term, and the rate of interest on the borrowed sum.
The U.S. Federal Government finances a lot of its debt with short-term borrowing, through Treasury bills (or T-Bills) (which mature in one year or less) and Treasury notes (or T-Notes) (which mature in 2-10 years). This means that much of the government debt is rolled over every year. This is where the issue of interest rates comes in in this context.
If the government had more of its debt held in longer term securities, such as Treasury bonds (T-Bonds, or the long bond), which have the longest maturity, from twenty years to thirty years…then fluctuating interest rates would have much less impact of the governments’ budget, as the payment schedule would be set for many years. This is what people mean when they say “lock in” a certain interest rate. It means to take out a long term loan at a fixed rate of interest, so that you know exactly what your debt service payments will be for many years into the future, regardless of how interest rates move.
However, if the government has to take out new loans every year, because so much of the debt is short-term, it means that they are subject to new contracts…with new terms based on the new going rates of interest. If the interest rate is higher this year than it was last year, your new debt service payments will be higher than they were in the past…meaning you’ll have to find a way to cover a higher expense.
The issue that people are worried about is that the US government does not have the capacity to shoulder any more in debt service payments. The government is broke as it is. And the people are broke too. There simply isn’t enough wealth to pay the bills even if it was all taxed away.
So the only way for the government to cover higher debt service payments would be to print the money (i.e. create it out of thin air). This is exactly what governments of the past have done, which led to virtually all the great hyperinflations of the past.
When you say “declare bankruptcy”, what that refers to is basically one of the other two options, which is namely defaulting on the debt. (Essentially printing the money to pay is defaulting as well, because the money that is paid to the creditors becomes worthless anyway, so you are really defaulting there just the same. They get their “money”, but they still don’t have their purchasing power returned to them…and of course purchasing power is really the only thing that matters. I’ll give you all the money you want, so long as I get to decide the purchasing power.) But the government could very well just say “we’re not paying you.” (It’s unlikely for this to happen, as throughout history governments have virtually always elected for the hyperinflation route, but it’s a possible course of action nonetheless.)
People say the government is already bankrupt because it is understood by many that it is economically/mathematically impossible for the government to legitimately pay off the debt it has incurred.
Here’s a segment from a video which mentions the scenario of interest rates rising to the level they hit back in the 80s under Fed Chairman Volcker.