You are the treasurer of a company. Due to prior commitments associated with the purchase of office buildings, you are obliged to arrange for the following series of future payments: Today Year 1 $1M Year 2 $2M Year 3 $3M Year 4 $4M Year 5 $5M *Assume annual compounding. The term structure is flat at r = 6%. In order to prepare for these outlays you decide to invest in a portfolio of 3-year 4% coupon bonds and 5-year 8% coupon bonds. Both bonds have a face value of $1000 and pay coupons annually. How many bonds of each type should you buy, not only to fund the obligation but also to insure against having to invest more in the future to make up for any shortfall if rates change (i.e., to limit your interest rate risk)?