Question $14(5$ points$)$

You have the following information on three zero coupon bonds: Bond $1$: time to

maturity: $1$ year, face value $=$$$1,000,$ bond price $=$$$952\mathrm{.}36$; Bond $2$ : time to

maturity: $2$ years, face value $=$$$1,000,$ bond price $=$$$905\mathrm{.}68$; Bond $3$: time to

maturity: $3$ years, face value $=$$$1,000,$ bond price $=$$$852\mathrm{.}14.$ Part A: Calculate the

one, two and three year spot rates. Part B: Calculate the forward rate over the

second year and the forward rate over the third year. Round to at least $2$ decimals.