3.1. A 20 year endowment of $6000 issued to a life aged 40 is purchased by annual premiums. Obtain the Zillmer maximum for the insurance. Find the modified net premiums if an initial expense of $100 is paid from the first premium. Furthermore, derive the expressions for the modified net premium reserves at duration t = 1,2,. .. ,20 and evaluate them numerically at t = 1, t = 10, and t = 20. Use a 6% annual rate of interest.