$1)$ Given the anticipated rate of inflation $($i$)$ of $1\mathrm{.}7\%$ and the real rate of interest $($R$)$ of $1\mathrm{.}4\%,$ find the nominal rate of interest $($r$).$

$2)$ Given the rate information in the table below, estimate the nominal rate for a AA$-$rated corporate bond. Assume a liquidity premium of $8$ basis points. Identify as part of your answer the inflation risk premium, the default risk premium, the maturity premium, and the liquidity premium.

$3-$month T$-$bills $2\mathrm{.}0\%$

$30-$year Treasury bonds $5\mathrm{.}0\%$

AA$-$rated corp. bonds $8\mathrm{.}0\%$

Inflation Rate $1\mathrm{.}0\%$

$3)$ An investor buys a $20-$year Bbb$-$rated corporate bond with a nominal annual rate of return of $10\%.$ The average inflation rate is expected to be $2\%.$ The default risk premium is expected to be $5\%$ and the maturity premium is $4\%.$ Calculate the real rate of interest.

$4)$ The current rate of return on a one$-$year U$.$S$.$ Government security is $3\%.$ The rate of return on a two$-$year U$.$S$.$ Government security is $5\%.$ According to the expectations theory, what is the return on a one$-$year U$.$S$.$ Government security purchased one year from today?

$5)$ The date today is January $1,2010.$ A one$-$year security maturing on $1/1/11$ yields $3\%.$ A two$-$year security maturing on $1/1/12$ yields $6\%.$ A three$-$year security maturing on $1/1/13$ yields $11\%.$ Calculate the expected annual return on a two$-$year security beginning $1/1/11$ and maturing on $1/1/13.$