Consider a bond with $10\%$ coupon rate semiannually, $10-$year maturity, and with $$100$ par value. Please answer the following questions:

$(1)$ Explain the process of using yield curve $($shown in exhibit $5-5)$ to construct theoretical spot rate curve $($shown in exhibit $5-6)?$

$(2)$ Please calculate the spot rate for periods of six months, twelve months, eighteen months, and twenty$-$four months?

$(3)$ What is the bond price by using yield curve shown in Exhibit $5-5?$

$(4)$ What is the bond price by using theoretical spot rate shown in Exhibit $5-6?$

$(5)$ What will the arbitraging profit the dealer creates?

$(6)$ What is the annual forward rate starting month $30$ and ending month $36,$ using data in Exhibit $5-6?$