# If all 40 year old policyholders are in the same risk

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If all 40-year-old policyholders are in the same risk class, each would be asked to pay the following amount in annual premiums: Expected claims/Number of Policyholders = \$15,000,000/10,000 = \$1,500 If the company wished to cover all operating expenses plus a target profit, it must charge an additional amount to each policyholder of: (Total operating Expenses + Profits)/Number of Policyholders = \$500,000/10,000 = \$50 Thus, the total annual premium, including both full cost recovery and coverage of benefit claims, is \$1,550.
2. A pension fund has accumulated \$1 million in a retirement plan for James B. Smith, who retired this month at age 65. If Mr. Smith has a life expectancy of 75 years, what is the minimum size of the annual annuity check the pension plan will be able to send him each year (assuming that the value of the pension fund’s investments remains stable)? Should he insist on receiving that size payment each year? Why or why not? What other kinds of information would be helpful in analyzing Mr. Smith’s financial situation at retirement?
Chapter 16 - Mutual Funds, Insurance Companies, Investment Banks, and Other Financial Firms ANSWER: If Mr. Smith is expected to need retirement income for 10 more years to age 75, he could ask to receive: Annual required income = \$1 million /10 years = \$100,000 per year However, this is risky because he may live beyond the age of 75. If he drains \$100,000 per year automatically, the fund will be dangerously low in 10 years. One important piece of information missing here is how much interest Mr. Smith’s retirement fund will accumulate each year. Even if he takes out \$100,000 at the opening of the first year of his retirement program, he will earn interest income on \$900,000 during the first year. If the average return on those funds is 10 percent, he will earn \$90,000 in interest by the end of the first retirement year, giving him an account balance of \$990,000. At the beginning of the second year he could draw out another \$100,000, leaving a balance of \$890,000. Clearly his accumulated wealth is falling, but much more slowly than a straight-line approach would suggest because of the compound interest factor. There are at least three other factors that have not been considered in the foregoing discussion. These are: a. the expected rate of inflation over the retirement period; b. Mr. Smith’s tax situation, especially his income tax bracket so we can determine how much “take home” income he will receive; and c. whether Mr. Smith has mandatory expenses (such as medical bills) which must be paid each year, limiting his discretion over exactly how much income he can draw out of the retirement fund each year.