11 (3 points) 900 people, all of the same age, have purchased whole life insurance that pays $200,000 at the end of the year in which death occurs. They have each purchased this with an annuity due with payments at the beginning of each year of their lives. The APV of the gross payments is equivalent to the APV for the gross benefits and expenses. You are given that the expectation of the gross loss squared, E[(Lo8)2] is 150,000,000. At the 95th percentile, what is the present value of the amount the insurance company could lose on this portfolio of policies? For your convenience, a table of the cumulative standard normal distribution is given: Cumulative standard normal Inverse normal N(z) 2 N(2) N(z) Z 4 0.00003 0.25 0.59871 99.5% 2.575829 -3.75 3.5 0.00009 0.00023 0.5 0.69146 99% 2.326348 0.75 0.77337 97.5% 1.959964 -3.25 0.00058 1 0.84134 95% 1.644854 3 0.00135 -2.75 0.00298 1.25 0.89435 1.5 0.93319 90% 1.281552 80% 0.841621 -2.5 0.00621 1.75 0.95994 -2.25 0.01222 2 0.02275 -1.75 0.04006 2 0.97725 2.25 0.98778 2.5 0.99379 75% 0.67449 70% 0.524401 5086 1.5 0.06681 2.75 0.99702 -1.25 0.10565 -1 0.15866 0.75 0.22663 -0.5 0.30854 3 0.99865 3.25 0.99942 3.5 0.99977 3.75 0.99991 -0.25 0 0.40129 0.50000 4 0.99997 4.25 0.99999 30% 0.5244 25% 0.67449 20% -0.84162 10% 1.28155 5% -1.64485 2.5% 1.95996) 1% 2.32635 0.5% -2.57583