Consider a $2-$year, risk$-$free bond with a coupon rate of $5\%($annual coupons$)$ and a face amount of $$1,000.$

a$.$ What is price of this bond if the YTM is $4\%?5\%?6\%?$

b$.$ If you buy the bond for $$1,000($YTM $=5\%,$ hold it to maturity and you reinvest the coupon payment at $4\%,$ what is the annual HPR on your investment?

c$.$ If you buy the bond for $$1,000($YTM $=5\%),$ then the yield increases to $6\%,$ and you sell the bond immediately after the first coupon payment $($in $1$ year$),$ what is your HPR$?$

d$.$ If the yield on the bond is $)=($$$1,000,$

i$.$ What is the Macaulay duration?

ii$.$ If the yield increases to $6\%$ immediately, what does the duration approximation predict will be the percentage change in the bond price?

iii. If the yield increases to $6\%$ immediately, what is the actual percentage change in the bond price?