A Treasury note with a maturity of four years carries a nominal rate of interest

Question

A Treasury note with a maturity of four years carries a nominal
rate of interest of 10 percent. In contrast, an eight-year Treasury
bond has a yield of 8 percent.
a. If inflation is expected to average 7 percent over the first four
years, what is the expected real rate of interest?
b. If the inflation rate is expected to be 5 percent for the first
year, calculate the average annual rate of inflation for years
2 through 4.
c. If the maturity risk premium is expected to be zero between
the two Treasury securities, what will be the average annual
inflation rate expected over years 5 through 8?

I am mostly having trouble with part c. I found other posts with solutions but I dont really understnad the steps to get there.

Explanation / Answer

c) Y4 = real rate + Inflation4 10% = real rate +7% real rate = 3% Y8 =real rate + Inflation8 8% =3% +Inflation8 Inflation8= 5% Inflation8 =average annual inflation rate over years 1 through 4 +average annual inflation rate expected over years 5 through 8 5% =7% +average annual inflation rate expected over years 5 through 8 average annual inflation rate expected over years 5 through 8 = -2% Answer -2%

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