Q$4($Essential to cover$)$ Consider the following bonds:

$$ Bond A: A $2-$year zero$-$coupon bond with a face value of $$100$ and $6\%$ YTM$.$

$$ Bond B: A $2-$year par$-$value bond with a face value of $$100$ and $6\%$ coupon.

$$ Bond C: A $2-$year par$-$value bond with a face value of $$100$ and $7\%$ coupon.

$$ Bond D: A $3-$year par$-$value bond with a face value of $$100$ and $7\%$ coupon.

$$ Bond E: A $4-$year par$-$value bond with a face value of $$100$ and $7\%$ coupon.

$$ Bond F: A $4-$year discount bond with a face value of $$100$ and $7\%$ coupon.

If the yield curve shifts upwards by one percent,

a$.$ Which bond among bonds A$,$ B and C will experience the largest percentage price change? Which will have the lowest percentage price change?