With t measured in years, an annuity makes payments Pt at the following continuous rates:

3t 6, 2 t 12 54 2t, 12 t 27

Given i = 0.075, what is the PV of this annuity at time 0? (Hint: find PV of the first increasing part at time t = 2 and then adjust to time t = 0; find PV of the second decreasing part at time t = 12 and then adjust to time t = 0)