Suppose a CLO on $100M of loans is structured with 70% senior, 20% mezzanine, and 10% equity tranches. The loans pay 7% fixed and there is a 3% risk of default with a loss of 20% when default occurs. The senior tranche pays 4% fixed, and the mezzanine 8% fixed. This matches the lecture example so far, and you will have seen the equity tranche expects to earn 17.9% based on these figures. Now suppose the loans are for 30 years and all payments are annual at the end of each year for the 30 years. Suppose also that any 1% increase in interest rates generally causes a 1% increase in the default rate in a linear fashion (so 3% would become 496). The three tranches are currently valued at par. Calculate the duration of each tranche.