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This is your homework assignment for the week of April 16, 2018. There will be no classes held that week. This assignment is due to me in hard copy (no emails) at the beginning of class on April 23, 2018. No exceptions on this due date, you have plenty of notice. You are permitted to work in groups on this assignment. Turn in one paper for each group.

80 points possible.

- (10 points) How long will you live?

- Go to https://www.johnhancockinsurance.com/life/life-expectancy-tool.aspx and calculate your life expectancy. Print the results, put your name on it and attach it to your response to these questions.
- Go to wwwssa.gov. Find the SS Life Expectancy Calculator. Enter your information and have it calculate your life expectancy. Print the results, put your name on it and attach it to your response.
- Is there a difference in your life expectancy on the two charts? Why do you think there is a difference in the results?

- Use the data from the tables on pages 465 – 468 in your text to answer the next series of questions.

- (2 points) If you started with a pool of 10,000,000 insureds, how many are expected to be aliveto reach age 40?

- Answer the following questions.Assume that you provide a one-year term insurance policy with a $5,000 death benefit to each of those persons who reach 40.

- (2 points) What is the number of deaths you expect to have in the year that those people are age 40?

- (2 points) What is the total death benefit you expect to pay in that year? Show me your calculations.

- (4 points) What is the premium you need to charge each insured to cover the death benefit? Show me your calculations.

- In addition to the net rate you have just calculated which covers the mortality costs, an insurer must cover such things as reserves, taxes, and expenses.

- (2 points) What is the term used to describe these additions to the cost of the insurance?

- (4 points) If the insurer expects to incur $500,000 in expenses, to pay $400,000 in taxes and must put $200,000 into reserves, how does that affect the premium to be charged that you calculated above? Show me your calculations.

- (4 points) Check your lecture notes for the discount rate to take into consideration that the premium is paid in advance on January 1
^{st}and all deaths are presumed to occur on December 31^{st}. If you find that rate, what is the discounted net premium (the net rate) the insurer can charge and still have enough money to pay the promised death benefit? Show me your calculations.

- (4 points) In order to compare the relative cost of insurance protection from different companies or different policies, we reduce the premium on an insurance policy to a “cost per thousand.” What is the cost per thousand for the policy you calculated above? Show me your calculations.

- Assuming the facts above, what would be the consequence to the insurer:

- (4 points) If there were 16,000 deathsin the year?

- (4 points) If there were 15,000 deaths in that year?

** **

- (20 points) Refer to page 465 of your text. This question is intended to use the Law of Large Numbers to show you how important it is for an insurer to make extremely accurate estimates about MIX-P. “Accurate estimates” means that the insurer’s actual results do not deviate very much from its expected results. Focus on just one MIX-P element – mortality. The table on page 465 indicates an
__expectation__that the probability of death during the year following a person’s 25^{th}birthday is 0.00107. Applied to a pool of 9,856,681 insureds (a very large number) who have reached that age out of the 10,000,000 at the beginning, we can expect 10,547 deaths during that year. In the questions above you have shown me that you know how to calculate the premium based on that mortality expectation. Assume that the insurer has sold a one-year term policy with a $100,000 death benefit to all of its insureds on their 25^{th}__Your assignment: Now calculate the consequences to the insurer if actual mortality deviates from expected mortality and increases (that means more people died than you expected) by only 0.00093 (that’s a very small deviation). Show me your calculations.__

__ __

- Without cutting and pasting an answer from somewhere on the internet, but in your own words and without quoting anything from anywhere, answer the questions below. If you absolutely have to quite something, ok, but then you must cite your source and explain the quotation to me in your own words. The goal here is to show me that you understand the concept, not that you can find an explanation written by someone else.

- (5 points) Explain why it is desirable for Surplus Adequacy Ratios and Rate of Surplus Formation ratios to be greater than one.

- (5 points) A leverage ratio tells us how much debt an insurer has relative to its surplus. Explain the advantages and risks of leverage for an insurer.

- (8 points) Without cutting and pasting an answer from somewhere on the internet, but in your own words and without quoting anything from anywhere, answer the questions below. If you absolutely have to quite something, ok, but then you must cite your source and explain the quotation to me in your own words. The goal here is to show me that you understand the concept, not that you can find an explanation written by someone else. A life insurance policy is a (1) unilateral, (2) conditional, (3) valued (i.e., not indemnity), (4) contract of adhesion. What is the meaning of each term?

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