You are in charge of the bond trading and forward loandepartment of a large investment bank. You have the following YTM’sfor five default-free pure discount bonds as displayed on yourcomputer terminal: Years of Maturity 1 2 3 4 5 YTM 0.06 0.065 0.070.065 0.08 Where YTM denotes the yield to maturity of a defaultfree pure discount bond (zero coupon bond) maturing at year j. a) Anew summer intern from Harvard has just told you that he thinksthat 3 year treasury notes with annual coupons of $100 and facevalue of $1,000 are trading for $1,000. Would you ask the intern torecheck the price of this coupon bond? If so, why? If there is oneactually traded for $1,000, how would you take this opportunity? b)A client approaches you looking for an annualized quote on aforward loan of $5 million dollars to be received by the customerat the end of the third year and she will repay the loan at the endof the fifth year. How would you structure your holdings of purediscount bonds so you can exactly match the future cash flows ofthis loan? Please indicate the number of bonds to be purchased orsold and the involved cost/benefit in dollar terms. What is thecorresponding annualized forward interest rate you quote for yourclient? c) Suppose that you purchased the bond in part 1(a) at theprice you calculated. It is now one year later and you justreceived the first coupon payment on the bond. At this time, theyield to maturities up to 3 year pure discount bonds are Years tomaturity 1 2 3 4 5 YTM 0.08 0.095 0.09 0.075 0.06 If you were tosell the bond now, what rate of return would you realize on yourinvestment in the bond?