Both Bond Sam and Bond Dave have $8$ percent coupons, make semiannual payments, and are priced at par value. Bond Sam has $5$ years to maturity, whereas Bond Dave has $18$ years to maturity. $($Do not round your intermediate calculations.$)$

Requirement $1$:

$($a$)$ If interest rates suddenly rise by $3$ percent, what is the percentage change in the price of Bond Sam?

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$($b$)$ If interest rates suddenly rise by $3$ percent, what is the percentage change in the price of Bond Dave?

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Requirement $2$:

$($a$)$

If rates were to suddenly fall by $3$ percent instead, what would the percentage change in the price of Bond Sam be then?

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$($b$)$

If rates were to suddenly fall by $3$ percent instead, what would the percentage change in the price of Bond Dave be then?

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