Higher inflation, lower real interest rate, why?

The correction answer is A because the answer states " an increase in New Zealand’s inflation rate will decrease its real interest rate and lead to the real interest rate differential favoring Japan over New Zealand…"

My question: If the inflation rate is higher, will the nominal interest rate be higher? Why are we assuming the nominal rate stays the same so that the real interest rate is lower?

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Nominal rates will rise to a certain point, but consider investments in non-inflation protected treasuries, you will have positions that are being hindered due to an increase inflation - yields are rising your bonds are decreasing in value. An increase in nominal rates can’t just happen overnight.

Good real world view of high inflation and real rates: https://www.stlouisfed.org/on-the-economy/2015/november/will-real-yields-decline-further

Great article! Thanks for the help!!

Just think PPP