Both Bond Sam and Bond Dave have $8$ percent coupons, make semiannual payments, and are priced at par value. Bond Sam has $4$ years to maturity, whereas Bond Dave has $15$ years to maturity.

If interest rates suddenly rise by $4$ percent, what is the percentage change in the price of Bond Sam?

multiple choice $1$

$12\mathrm{.}78\%$

$-12\mathrm{.}42\%$

$-14\mathrm{.}18\%$

$-12\mathrm{.}40\%$

If interest rates suddenly rise by $4$ percent, what is the percentage change in the price of Bond Dave?

multiple choice $2$

$-27\mathrm{.}53\%$

$-37\mathrm{.}99\%$

$-27\mathrm{.}51\%$

$30\mathrm{.}94\%$

If rates were to suddenly fall by $4$ percent instead, what would the percentage change in the price of Bond Sam be then?

multiple choice $3$

$12\mathrm{.}78\%$

$14\mathrm{.}65\%$

$14\mathrm{.}63\%$

$-12\mathrm{.}37\%$

If rates were to suddenly fall by $4$ percent instead, what would the percentage change in the price of Bond Dave be then?

multiple choice $4$

$44\mathrm{.}77\%$

$-27\mathrm{.}48\%$

$44\mathrm{.}79\%$

$30\mathrm{.}94\%$