Both Bond Sam and Bond Dave have $3$ percent coupons, make semiannual payments, and are priced at par value. Bond Sam has $4$ years to maturity, whereas Bond Dave has $8$ years to maturity.

a$)$ If interest rates suddenly rise by $1\%$ point, what is the percentage change in the price of Bond Sam?

b$)$ If interest rates suddenly rise by $1\%$ point, what is the percentage change in the price of Bond Dave?

c$)$ If interest rates suddenly fall by $1\%$ point instead, what is the percentage change in the price of Bond Sam?

d$)$ If interest rates suddenly fall by $1\%$ point instead, what is the percentage change in the price of Bond Dave?