Consider a three$-$year coupon bond with a face value of $$1000$ and a coupon rate of $5\%.$ Assume the interest rates follow the path from Node $0$ to Node $2$ to Node $5$ so that one$-$year interest rates are $4\%,3\%,$ and $2\%.$

$4.$ What is the price or present value of the bond?

$5.$ What is the bond's yield to maturity$($annual equivalent yield$)?$