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CH. 7 PLANNING AHEAD CH. 7 PLANNING AHEAD 7-1 Life Insurance: Who needs it?7-1 Life Insurance: Who needs it? 7-2 Spreading the Risk: How Insurance works7-2 Spreading the Risk: How Insurance works 7-3 Value for the Future7-3 Value for the Future

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Chapter 7-2 SPREADING THE RISK: HOW INSURANCE WORKS

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OBJECTIVES Understand how life-expectation tables are used to estimate the probability that an individual will die within one year.Understand how life-expectation tables are used to estimate the probability that an individual will die within one year. Learn how an insurance company determines its premium schedule to make a reasonable profit.Learn how an insurance company determines its premium schedule to make a reasonable profit.

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Probability of an Event P(E) = m/n Where P(E) = the probability of an event E m = the number of times the event occurs n = the number of all possible outcomes

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Example Using the chart on page 331 of your textbook, find the probability of a 16-year old person will be alive 1 year from today. # of 16-year old people alive 1 year later Total number of 16- year old people 99,921 99,921 100,000 =.99921

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P(E‘) = Probability of a 16-year old will die in 1 year Total number of 16-year old people P(E‘) = 79 =.00079 100,000 The sum of the probabilities of an event and its complement is 1 P(E) + P(E‘) = 1

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Expected Value is the amount of money to be won or lost in the long run. If an event can assume two values, then the expected value of the event is the sum of the product of each value and its probability. EXPECTED VALUE FORMULA E = P 1 v 1 + P 2 v 2 Where v 1 and v 2 are values and P 1 and P 2 are the corresponding probabilities

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Try Your Skills Example 1 The expected gain from a coin toss that pays $3 for heads and $2 for tails. P =.5 P 1 =.5 P =.5 P 2 =.5 v = 3 v 1 = 3 v = 2 v 2 = 2 E =.5(3) +.5(2) = 1.50 + 1.00 = $2.50

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Try Your Skills Example 2 The expected gain from a roll of a die that pays $10 for a 6 or a 2 and $1 for any other result. P = 2/6 = 1/3 P 1 = 2/6 = 1/3 P = 4/6 = 2/3 P 2 = 4/6 = 2/3 v = 10 v 1 = 10 v = 1 v 2 = 1 E = (1/3)(10) + (2/3)(1) = 3.33 +.67 = $4.00

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Break-even value Break-even value is the value of the premium that gives zero profit after paying for all expenses. E + expenses = P 1 v 1 + P 2 v 2 Where v 1 and v 2 are values and P 1 and P 2 are the corresponding probabilities

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Example 2 The company has direct and indirect expenses of $25 for each policy that it issues. Find the premium that the company must charge to break even; that is, neither to make or lose money on this policy.E = 0 P 1 =.99906P 2 = 1 -.99906 =.00094 v 1 = xv 2 = x – 60000 0 + 25 =.99906x +.00094(x – 60000) 25 =.99906x +.00094x – 56.4 25 = 1x – 56.4 81.40 = x$81.40 is the premium to break even

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Profit on Insurance P = R – B – C P = profit R = revenue received as premiums B = benefits paid out C = costs or expenses

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Example 3 Use the profit for insurance formula and the table of expected deaths (page 331) to calculate the profit that a company makes on one-year term life insurance policies. The cost of each policy is $25. a.1000 19-year olds; face value: $100,000; Annual premium: $200 b. 5000 28-year olds; face value: $135,000; Annual premium: $350

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1000 19-year olds; face value: $100,000; Annual premium: $200 x = profit for each policy P = 1000x R = 1000(200) 103 = ? B = 1.03(100,000) 100,000 1000 C = 25(1000)? = 1.03 1000x = 1000(200) – 1.03(100,000) - 25(1000) 1000x = 72,000 x = 72; profit = 1000(72) = $72,000

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5000 28-year olds; face value: $135,000; Annual premium: $350 x = profit for each policy P = 5000x R = 5000(350) 127 = ? B = 6.35(135,000) 100,000 5000 C = 25(5000)? = 6.35 5000x = 5000(350) – 6.35(135,000) - 25(5000) 5000x = 767,750 x = 153.55; profit = 5000(153.55) = $767,750

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Assignment page 337 7-25 (use chart on page 676 for 22-25)

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© 2010 Pearson Prentice Hall. All rights reserved. CHAPTER 11 Counting Methods and Probability Theory.

© 2010 Pearson Prentice Hall. All rights reserved. CHAPTER 11 Counting Methods and Probability Theory.

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