how can a rise in inflation decrease the country debt value?

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Inflation in general makes debts go down in value.

If, today, you have a debt that is listed as $10,000 and that debt is equivalent to 3,500 loaves of bread or 6,000 hours of labor, then inflation comes along and makes the price of everything double, now your $10,000 debt is the equivalent of 1,750 loaves of bread or 3,000 hours of labor.

Since the dollars got less valuable the debt, despite being the same number of dollars, is worth less.

This effect actually being enough to reduce the value of any given debt depends on a few things. One is that the inflation has to run faster than the debt accrues interest. Most private loans won’t fall into this category, but for example some mortgages that were set with ~2.5% APR are enjoying inflation right now. For an individual to enjoy this effect they also need to see their wages keep pace with inflation, though typically wages lag behind as workers have a harder, slower time at renegotiating wages than companies have with simply raising prices in stores.

National debt tends to come in at some of the lowest interest rates seen in the economy and often terms are in the tens of years. Also, a nation’s income comes from the income across the economy from individuals and businesses, so a nation’s income will tend to track inflation more readily than an individual’s. This makes it much easier for national debt to go down in value when there’s inflation than a private debt.

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