Suppose the current one$-$year interest rate is $5\mathrm{.}9\%.$ One year from now, you believe the economy will start to slow and the one$-$year interest rate will fall to $4\mathrm{.}9\%.$ In two years, you expect the

economy to be in the midst of a recession, causing the Federal Reserve to cut interest rates drastically and the one$-$year interest rate to fall to $1\mathrm{.}9\%.$ The one$-$year interest rate will then rise fo

$2\mathrm{.}9\%$ the following year, and continue to rise by $1\%$ per year until it returns to $59\%,$ where it will remain from then on$.$

a$.$ If you were certain regarding these future interest rate changes, what two$-$year interest rate would be consistent with these expectations?

b$.$ What current term structure of interest rates, for terms of $1$ to $10$ years, would be consistent with these expectations?

c$.$ How does the one$-$year interest rate compare to the ten$-$year interest rate?

b$.$ What current term structure of interest rates, for terms of $1$ to $10$ years, would be consistent with these expectations?

Fill in the missing values in the following table: $($Round the FV to four decimal places and the EAR to two decimal places.$)$