You find a zero coupon bond with a par value of $$10,000$ and $18$ years to maturity. The yield to maturity on this bond is $5$ percent. Assume semiannual compounding periods. What is the price of the bond?

Note: Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$

Both Bond Sam and Bond Dave have $9\mathrm{.}2$ percent coupons, make semiannual payments, and are priced at par value. Bond Sam has $4$ years to maturity, whereas Bond Dave has $21$ years to maturity. Both bonds have a par value of $1,000.$

If interest rates suddenly rise by $3$ percent, what is the percentage change in the price of these bonds?

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$.,32\mathrm{.}16.$

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

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