Problem $2(20$ points$)$: Evaluate the following pure$-$yield pickup swap: You currently hold a $20$yearm AA$-$rated, $9\%$ coupon rate bond with yield to maturity of $11\mathrm{.}0\%,$ and face value $$1,000.$ As a swap candidate, you are considering a $20-$yearm AA$-$rated, $11\%$ coupon rate bond with yield to maturity of $11\mathrm{.}5\%,$ assume reinvestment rate is $11\mathrm{.}5\%$ and coupon are paid semiannually, please fill out the table below and you must show $($explain$)$ clearly how numbers in the table are obtained.

Current Bond

Candidate bond

$\backslash$table$[[$Dollar investment,,$],[$Coupon$,,],[$i on one coupon,,$],[$Principal value at year end,,$],[$Total accrued,,$],[$Realized compound yield,,$],[$Value of swap:,,basis point in one year$]]$