Your $100 million bond portfolio has currently $90 million invested in bonds and the remainder invested in T bills. The duration of the bond component is 5.2 years. Assume that the T bond futures contract has a duration of 7.8 years and a value of $102,500 per contract

Q) How many futures contracts should be purchased or sold to change your portfolio's duration to 6.0 years? and How many futures contracts should be purchased or sold in order to make the portfolio insensitive to changes in interest rates?