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8.3 Expected Value

8.3 Expected Value
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  • 1. Expected Value of Life Insurance

    The table shows the probabilities of dying during the year for various ages.

    A 23-year-old male pays $275 for a 1-year $150,000 life insurance policy. What is the expected value of the policy for the policyholder? (See Example 1 and Example 2.)

    • Worked-Out Solution

      It makes sense that the expected value is negative. Remember that this is from the point of view of the policyholder. This means that the expected value for the insurance company is positive. Another way to think of this is that the insurance company can expect to earn about $50 for each 23-year-old male that buys a 1-year $150,000 policy.

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     _____     _    _     _____      ___     _____    
    |  __ \\  | || | ||  / ____||   / _ \\  |  __ \\  
    | |  \ || | || | || / //---`'  | / \ || | |  \ || 
    | |__/ || | \\_/ || \ \\___    | \_/ || | |__/ || 
    |_____//   \____//   \_____||   \___//  |_____//  
     -----`     `---`     `----`    `---`    -----`   
                                                      
    
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  • 2. Expected Value of Life Insurance

    The table shows the probabilities of dying during the year for various ages.

    A 28-year-old female pays $163 for a 1-year $200,000 life insurance policy. What is the expected value of the policy for the policyholder? (See Example 1 and Example 2.)

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       _____     ___     _    _    _    _   __    __  
      / ___//   / _ \\  | || | || | || | || \ \\ / // 
      \___ \\  / //\ \\ | || | || | || | ||  \ \/ //  
      /    // |  ___  ||| \\_/ || | \\_/ ||   \  //   
     /____//  |_||  |_|| \____//   \____//     \//    
    `-----`   `-`   `-`   `---`     `---`       `     
                                                      
    
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  • 3. Expected Value of Life Insurance

    The table shows the probabilities of dying during the year for various ages.

    A 27-year-old male pays $310 for a 1-year $175,000 life insurance policy. What is the expected value of the policy for the insurance company? (See Example 1 and Example 2.)

    • Worked-Out Solution

      Notice that this is from the point of view of the insurance company.

      It makes sense that the expected value is positive. Another way to think of this is that the insurance company can expect to earn about $70 for each 27-year-old male that buys a 1-year $175,000 policy.

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      _____     _____     _____      ___      _____   
     |__  //   |  ___||  / ____||   / _ \\   / ____|| 
       / //    | ||__   / //---`'  | / \ || / //---`' 
      / //__   | ||__   \ \\___    | \_/ || \ \\___   
     /_____||  |_____||  \_____||   \___//   \_____|| 
     `-----`   `-----`    `----`    `---`     `----`  
                                                      
    
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  • 4. Expected Value of Life Insurance

    The table shows the probabilities of dying during the year for various ages.

    A 25-year-old female pays $128 for a 1-year $120,000 life insurance policy. What is the expected value of the policy for the insurance company? (See Example 1 and Example 2.)

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     _    _    _    _    _    _     ______     _____  
    | |  | || | || | || | \  / ||  /_   _//   / ___// 
    | |/\| || | || | || |  \/  ||   -| ||-    \___ \\ 
    |  /\  || | \\_/ || | .  . ||   _| ||_    /    // 
    |_// \_||  \____//  |_|\/|_||  /_____//  /____//  
    `-`   `-`   `---`   `-`  `-`   `-----`  `-----`   
                                                      
    
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  • 5. Expected Values

    The table shows the probabilities of dying during the year for various ages.

    A 26-year-old male pays $351 for a 1-year $180,000 life insurance policy. (See Example 1 and Example 2.)

    1. What is the expected value of the policy for the policyholder?
    2. What is the expected value of the policy for the insurance company?
    3. Suppose the insurance company sells 10,000 of these policies.

      What is the expected value of the policies for the insurance company?

    • Worked-Out Solution
      1. Notice that this is from the point of view of the policyholder.

      2. The expected value for the insurance company is $100.26.
      3. If the insurance company sells 10,000 of these policies, it can expect to earn

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     _    _      ___      ______   _    _     ______  
    | \  / ||   / _ \\   /_   _// | || | ||  /_____// 
    |  \/  ||  / //\ \\  `-| |,-  | || | ||  `____ `  
    | .  . || |  ___  ||   | ||   | \\_/ ||  /___//   
    |_|\/|_|| |_||  |_||   |_||    \____//   `__ `    
    `-`  `-`  `-`   `-`    `-`'     `---`    /_//     
                                             `-`      
    
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  • 6. Expected Values

    The table shows the probabilities of dying during the year for various ages.

    A 30-year-old female pays $259 for a 1-year $250,000 life insurance policy. (See Example 1 and Example 2.)

    1. What is the expected value of the policy for the policyholder?
    2. What is the expected value of the policy for the insurance company?
    3. Suppose the insurance company sells 10,000 of these policies. What is the expected value of the policies for the insurance company?
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    These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.
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                 ___      _____      ___      _____   
      ____      / _ \\   / ____||   / _ \\   /  ___|| 
     |    \\   | / \ || / //---`'  | / \ || | // __   
     | [] ||   | \_/ || \ \\___    | \_/ || | \\_\ || 
     |  __//    \___//   \_____||   \___//   \____//  
     |_|`-`     `---`     `----`    `---`     `---`   
     `-`                                              
    
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