Both Bond Sam and Bond Dave have $6\mathrm{.}5$ percent coupons, make semiannual payments, and are priced at par value. Bond Sam has $3$ years to maturity, whereas Bond Dave has $20$ years to maturity. If interest rates suddenly rise by $2$ percent, what is the percentage change in the price of Bond Sam? Of Bond Dave? If rates were to suddenly fall by $2$ percent instead, what would the percentage change in the price of Bond Sam be then? Of Bond Dave? All bond price answers should be dollar prices.

Bond Sam:

Coupon rate

Settlement date

Maturity date

Redemption $(\%$ of par$)$

# of coupons per year

$6\mathrm{.}5\%\frac{1}{1}\frac{?}{2000}$

$\frac{1}{1}\frac{?}{2003}$

$100$

$2$