Given the following prices of zero$-$coupon bonds with various maturities:

Year Price $(\%)$

$195\mathrm{.}238$

$290\mathrm{.}27257$

$385\mathrm{.}16137$

$479\mathrm{.}96105$

$574\mathrm{.}72582$

a$)$ Calculate the yields to maturity of each bond and the implied sequence of forward rates. What shape does the resulting yield curve have? Can both theories of the term structure of interest rates covered in the course explain this yield curve?

b$)$ Based on no arbitrageur argument, calculate the price of an $8\%,5-$year coupon bond using the yield curve in a$).$ What is this coupon bond's yield to maturity? Current yield? If at the end of the first year, the yield curve flattens out at $7\mathrm{.}5\%,$ what will be the $1-$year holding$-$period return on this coupon bond?

c$)$ Given these zero$-$coupon bond prices and$/$or your calculated forward rates in a$),$ how could you construct a $2-$year forward loan beginning in year $2?($Hint: today you issue enough amount $($in $$)$ of $4-$year zero$-$coupon bond in order to buy one $2-$year zero$-$coupon bond$).$ Draw a time line of cash flows for this strategy. What is the effective $2-$year interest rate on the effective $2-$year ahead forward loan?