You are considering buying a bond with a face value of $100,$ an annual coupon rate of $5\mathrm{.}50\%$ and a maturity of four years. The bond is callable at a price of $100.$ The one year forward interest rates are $3\%,4\%,5\%,$ and $6\%$ for years $1,2,3$ and $4$ respectively. a$.$ How much will the bond be worth today? b$.$ If the bond can be put at par how much is the bond worth today? c$.$ What do you notice about interest rates when you choose to put the bond in part b$?$