(By “real terms,” I mean that the borrower has to give up a surprising amount of goods and services to be able to afford the repayments.) The FOMC can’t solve that problem today, of course. But if the FOMC uses inflation targeting, the borrower’s repayments are likely to remain surprisingly expensive in real terms even in 2042, 30 years after taking out the mortgage.
In contrast, if the FOMC uses price level targeting, the borrower’s repayments in 2042 are likely to be close, in real terms, to what the borrower expected when originally taking on the loan. The second reason that the FOMC might want to use price level targeting is that it would serve as an automatic stabilizer for the economy.