Please answer each part of this question with explanation of your work.

Question: JMC has just issued a new annual coupon bond that has 5 years to maturity, a coupon rate of 8% and trades at par at a price of $1000. You may assume that the yield-curve is flat. a) Compute the duration of the JMC bond. b) Estimate the dollar price change of the JMC bond using duration if interest rates increase by 0.5%. c) The government has recently issued five series of zeroes (zero-coupon bonds) with 6 month, 1 year, 18 month, 2 year and 30 month maturity horizons. If the bonds have respective prices of $967.16, $927.56, $889.05, $861.36 and $810.52 bootstrap the 1 year, 18 month and 2 year forward 6 month rates. d) Identify if the 6 month forward-rate curve you computed in c is in a state of backwardation, contango or is flat.