Problem $5-17$ Interest Rate Risk

Both Bond Sam and Bond Dave have $6$ percent coupon bonds outstanding, with semiannual interest payments, and both are currently priced at the par value of $$1,000.$ Bond Sam has four years to maturity, whereas the Bond Dave has $19$ years to maturity.

a$.$ If interest rates suddenly rise by $2$ percent, what is the percentage change in the price of each bond?

Note: A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$

b$.$ If rates were to suddenly fall by $2$ percent instead, what would be the percentage change in the price of each bond?

Note: Do not round intermediate calculations and enter your answers as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$

$\backslash$table$[[$a$.$ Percentage change in price of Bond Sam,$],[$Percentage change in price of Bond Dave,$\%$