The n n -year inflation rate, I n I n , is the growth rate in the

The $n$-year inflation rate, $I_n$, is the growth rate in the price of a basket of goods. In the United States, the Consumer Price Index (CPI) serves as the price index and is related to the inflation rate as

$$CPI\left(n\text{year}\right)=CPI\left(0\right)\times {(1+I_n)}^n$$

An often-used metric for inflation expectation is the 5-year, 5 -year forward inflation rate, $I_{5,5}$ backed out of market levels for $I_5,I_{10}$.

(a) By relating them to the annually compounding growth rate of CPI, provide a formula for $I_{5,5}$ in terms of $I_5,I_{10}$.

(b) Compute the 5 year-5 year forward inflation rate when $I_5=2\%$, $I_{10}=3\%$.