To help financing its green projects, a UK based company is issuing a number of new bonds. These bonds have a face value of $1,000,10\%$ coupon rate and $5-$year maturity. Assume that you can borrow from the risk$-$free market at the rate of $3\%$ and that the current short rate is $5\%$ but it is expected to be $4\%,5\%,$ and $6\%$ with probability $0\mathrm{.}3,0\mathrm{.}4$ and $0\mathrm{.}3,$ respectively. Compute possible values of the bonds. Also, compute possible values of the bonds if they are inflation protected. Assume that inflation rate is $1\%$ a year.