Please show work. An advantage of having nominal and real bonds traded at the same time is that they provide real time inflation expectations, while, for example, survey forecasts are usually available only once a month or once a quarter. To illustrate this point, suppose there is a zero-coupon two year US government real bond with the real par value of $1,000 trading at $970. There is also a 4 year zero-coupon US government nominal bond with the par value of $1,000 trading for $795. Assume that the real and inflation rates are constant over time, there are no taxes, and the liquidity and inflation risk premium are 0.

a) What is the annual inflation rate in the economy? Decompose the interest rate into the real and nominal components.

b) What is the nominal payment the holder of the 2 year zero-coupon real bond above will receive if there will be no default?