The table below shows the yield to maturity of the one$-$year TIP, one$-$year treasury bill, and the level of the CPI $[$Consumer Price Index: an index or "average" of price level for the economy$]$ as of January $1,2018$ and $2019.$

$\backslash$table$[[,$TIPS,$1$ yr$.$ bill,CPI$],[$Jan$\text{'}19,1\mathrm{.}00\%,2\mathrm{.}52\%,252\mathrm{.}6],[$Jan$\text{'}18,0\mathrm{.}35\%,1\mathrm{.}78\%,248\mathrm{.}8]]$

a$.$ What was the TIPS spread on Jan $1,2018?$ On Jan. $1,2019?$

b$.$ If an investor purchased a one$-$year bill January $1,2018$ and held it until maturity January $1,2019,$ what nominal yield did she realize?

c$.$ What was the inflation rate for the year of $2018?$

d$.$ If an investor purchased a one$-$year bill January $1,2018$ and held it until maturity January $1,2019,$ what real yield did she realize?

e$.$ If the investor believed the market data available when she bought the T$-$bill Jan. $1,2018,$ what nominal yield would she have been expecting to get?

f$.$ If the investor believed the market data available when she bought the T$-$bill Jan. $1,2018,$ what real yield would she have been expecting to get?