You spend $$985$ to buy a bond with $$1,000$ face value, $5\%$ coupon rate, and remaining maturity of $5$ years.

$(1)$ What will be the expected return if you plan to hold this bond to the maturity?

$(2)$ What will be your answer for part $(1),$ if the coupon interest is paid semi$-$annually?

$(3)$ If the yield to maturity changes to $4\mathrm{.}5\%$ right after you receive the second year coupon interest payment, and you decide to sell this bond, what should be the selling price?

$(4)$ What will be your two$-$year holding period return for part $(3)?$