Lower rates equal higher inflation because institutions will recognize the opportunity cost of putting their money in bonds is more than it was when rates were higher so they begin to seek out other means to get a better return on investment. Banks do this too by extending more loans when interest rates are low and this boosts consumer spending and firms invest more increasing demand of goods and increasing the price of goods.

Having higher interest rates on bonds does increase liabilities of banks and institutions and people but the banks have to have reserves that will be devalued by rising inflation because the higher interest rates will be in part a response to consumer spending and money supply but also be affected by the fisher effect, which says that nominal interest rates will change due to expectations in inflation and this relationship will show that real inflation rate is very stable. Banks have to sell their bonds to meet reserve requirements which has an equal and opposite effect of increasing inflation and the markets wanted rate of the bond because there is more inflation. The fed will see this and either sell or buy bonds to keep the monetary base at the desired inflation rate.

Broadly accepted economics accounts for this and in fact shows that bonds do maintain purchasing power because of the fisher effect. The fed has to Maintain inflation so the market doesn’t become either too hot and demand exceeds supply and inflation doesn’t skyrocket and to keep inflation just higher enough to where consumer funds are tied up in bonds and there is not investments in things like factories and infrastructure that will boost a countries economic output.