$2.$ Use the term structure of interest rates shown below represent the spot rates for

$1-,2-,3-,4-,$ and $5-$year zero$-$coupon bonds. below to solve question $2.$

Maturity $($years$)$ Zero Coupon aka Spot

Interest Rate

Discount Factor $($assuming

semi$-$annual

compounding$)$

$13\mathrm{.}5\%$

$23\mathrm{.}55\%$

$33\mathrm{.}60\%$

$43\mathrm{.}75\%$

$53\mathrm{.}80\%$

a$)$ Calculate the discount factor assuming semi$-$annual compounding. Show a

sample calculation for one of the numbers below:

b$)$ What are the current prices of a $5-$year zero$-$coupon bond and a $4-$year zero$-$

coupon bond each having a par value $=$ $$1,000?$

c$)$ What is the price of a bond that pays the following cash flows $($assuming semi$-$

annual compounding$)?$

$$50$ in years $1,2$ & $3$

$$1,000$ in year$-3$