$(20$ points$)$ You can buy or sell a $3\mathrm{.}000\%$ coupon $$1,000$ par U$.$S$.$ Treasury Note that matures in $5$ years. The first coupon payment pays $6$ months from now, and the Note pays coupons semi$-$annually until maturity. It also pays par on maturity. The Yield to Maturity of the Note right now $($treat this as your discount rate$)$ is $4\mathrm{.}000\%.$

$($a$)$ What are the cash flows associated with this Note?

$($b$)$ Which of these cash flows are annuity dues, ordinary annuities, or single cash flows?

$($c$)$ What is the present value of all payments associated with this Note?

$($d$)$ If interest rates move down, what would happen to the value of this Note?

$($e$)$ If a stranger was willing to buy or sell you the bond for $$1000,$ would you buy or sell it $-$ and why?

$($Hint: assume no altruism here.$)$