$1.$ You purchased a $7-$year $7\mathrm{.}5\%$ treasury bond five years ago for $98\mathrm{.}10.$ You sell it today for $103\mathrm{.}16($you received your $10$th and final coupon today$).$

a$.$ Determine your realized return $($APR$)$ from your investment.

b$.$ Determine the return the purchaser might expect to earn if she holds the bond until maturity and interest rates do not change during her ownership