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Interest typically has an inverse relationship with inflation, but in the US inflation and interest have been artificially low at the behest of the Federal Reserve because not only do they influence at what rate banks can lend money (interest) but they are also in charge of the printing of money (inflation). The main issue is that instead of allowing interest rates to rise during recessions the FED pushed interest rates artificially low (see dot-com bubble, housing bubble, COVID lockdowns) which did not allow a "healthy" recession to happen.
I can't remember when inflation rose significantly and the interest rates went down. I also don't remember a big rise in the inflation rate after the dot com bubble or the housing bubble. The last major inflation problem was in the 80's and interest rate and mortgage rate went high. I remember getting 8% on a one year CD and mortgage rates were above 10%.