Consider an investor initially purchases a $10-$year, $8\%$ annual coupon payment bond at a price of $$85\mathrm{.}503075$ per $$100$ of par value. The bond's yield to maturity $($YTM$)$ is $10\mathrm{.}40\%.$

$4.$ Assume the investor holds this bond until maturity. Also assume that the interest rates go down to $9\mathrm{.}40\%(100$ basis points decrease$)$ after the bond is purchased and before the first coupon is received. What is the investor's realized rate of return?

$5.$ Assume the investor sells this bond after four years. Also assume that the interest rates go down to $9\mathrm{.}40\%(100$ basis points decrease$)$ after the bond is purchased and before the first coupon is received. What is the investor's realized rate of return?