House prices would not be independent of interest rates if "interest rates represented market rates". House prices may be different but the math above still hol

House prices would not be independent of interest rates if "interest rates represented market rates". House prices may be different but the math above still holds. If interest rates are 1%, house prices are "high", because people can "afford more house". If interest rates go to 20%, house prices drop (by about 20%) because more of their money goes to interest. Your point that if the fed didn't control rates that somehow house prices would be independent of interest rates, but that's not how house prices work. What are you seeing that I'm not?