$15.$ A Consider two zero coupon bonds, $S$&$L$ that represent a short$-$term and long$-$term maturity bond respectively. The two bonds have the following features:

Bond $HC$: Maturity $=10$ years $PMT=,$$$40,$Par$=$$$1,000,YTM=,7\mathrm{.}00\%$ Price $=$$$789\mathrm{.}29$

Bond LC: Maturity $=10$ years $,PMT=,$$$20,$Par$=$$$1,000,YTM=,4\mathrm{.}00\%,$ Price $=$$$837\mathrm{.}78$

Which bond, the low$-$coupon bond LC or the high$-$coupon bond HC$,$ exhibits a greater price change when both yields increase by $1\%?$

Price of Bond $HC$ when $YTM=8\%$ :

Price change of $HC=$

Price of Bond LC when $YTM=5\%$ :

Price change of $LC=$

$16.$ A Consider two coupon bonds, HC and LC$,$ with the same maturity but the different coupon rate. HC$/$LC represent a High$/$Low Coupon, respectively. Assume m $=1.$ The two bonds have the following features:

Bond HC: Maturity $=10$ years PMT $=$ $$40$ Par $=$ $$1,000$ YTM $=7\mathrm{.}00\%$ Price $=$ $$789\mathrm{.}29$

Bond LC: Maturity $=10$ years PMT $=$ $$20$ Par $=$ $$1,000$ YTM $=4\mathrm{.}00\%$ Price $=$ $$837\mathrm{.}78$

Which bond, the low$-$coupon bond LC or the high$-$coupon bond HC$,$ exhibits a greater price change when both yields increase by $1\%?$

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