Both Bond Sam and Bond Dave have $7$ percent coupons, make semiannual payments, and are priced at par value $($you can assume this is $$1,000).$ Bond Sam has $4$ years to maturity, whereas Bond Dave has $12$ years to maturity.

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

multiple choice $1$

$-9\mathrm{.}69\%$

$-9\mathrm{.}67\%$

$9\mathrm{.}90\%$

$-10\mathrm{.}74\%$

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

multiple choice $2$

$-26\mathrm{.}10\%$

$-20\mathrm{.}68\%$

$-20\mathrm{.}70\%$

$22\mathrm{.}10\%$

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

multiple choice $3$

$-9\mathrm{.}64\%$

$10\mathrm{.}97\%$

$10\mathrm{.}99\%$

$9\mathrm{.}90\%$

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

multiple choice $4$

$28\mathrm{.}37\%$

$22\mathrm{.}10\%$

$28\mathrm{.}35\%$

$-20\mathrm{.}65\%$