Bond A pays $$8000$ in $20$ years. Bond B pays $$8000$ in $40$ years. For simplicity assume that both bonds are zero$-$coupon bonds, meaning the $$8000$ is the only payment the bondholder receives.

a$-$ If the interest rate is $3\mathrm{.}5\%,$ what is the value of each bond today? Which bond is worth more?

b$-$ If the interest rate increases to $7\%,$ what is the value of each bond. Which bond has a larger percentage change in value?