A person is about to retire at age 65. She has $1,000,000 in her retirement fund. For simplicity, we assume that the person will live 5, 10, 15 or 20 years after retirement. Actuarial data yields the following probabilities for these lifetimes. 10 yrs 15 yrs 20 yrs Additional life Probability 5 yrs 0.2 0.3 0.4 0.1 The insurance company holding the funds offers the two plans described below. Assume the first payment is at time 0 and will continue to be paid at the beginning of each year for the plan duration. Plan 1 is called the 20-year Certain Plan. Here the company will pay $100,000 a year for 20 years. These payments will occur whether the person lives or not. If the person dies during the 20-year period, her beneficiaries will continue to receive the payments for the remainder of the time. Plan 2 is called Lifetime Plan. Here the company will pay $120,000 a year for each year that the person lives. If she dies, her beneficiaries receive a lump sum payment of $120,000 at the beginning of the year following her death. No further payments are made. Compare the plans based on the NPW of the payments made by the insurance company. Compute the mean and standard deviation of the NPW for each plan. The person's MARR is 10%