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6.3 Home Mortgages

6.3 Home Mortgages
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  • 7. Amortization Schedules

    Use a spreadsheet. (See Example 3.)

    You take out a home mortgage for $238,000 for 30 years at 5%. Each month, you make the regular payment of $1277.64 plus an additional $60.

    1. How much sooner do you pay off the mortgage?
    2. How much do you save in interest?

    • Worked-Out Solution
      1. Use a spreadsheet to create an amortization schedule showing the effect of the additional monthly payment of $60.

        You will pay your mortgage off in 326 months. This is months earlier than if you make the regular payments.

      2. By making the regular monthly payments, you would pay

        With the additional payment of $60 per month, you will pay

        So, you willl save

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  • 8. Amortization Schedules

    Use a spreadsheet. (See Example 3.)

    You take out a home mortgage for $260,000 for 30 years at 6%. Each month, you make the regular payment of $1558.83 plus an additional $100.

    1. How much sooner do you pay off the mortgage?
    2. How much do you save in interest?

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      ______   _    _              __   __   _    _   
     /_   _// | || | ||     ___    \ \\/ // | || | || 
     `-| |,-  | || | ||    /   ||   \ ` //  | || | || 
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       |_||    \____//     \__ ||    |_||    \____//  
       `-`'     `---`       -|_||    `-`'     `---`   
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  • 9. Amortization Schedules

    Use a spreadsheet. (See Example 3.)

    You take out a home mortgage for $275,000 for 25 years at 4%.

    1. What is the least amount, to the nearest dollar, that you need to pay in addition to the regular payment to pay off the mortgage 5 years early?
    2. Compare the total interest you pay for the 25-year mortgage to the total interest you pay when you pay off the 25-year mortgage 5 years early.

    • Worked-Out Solution
      1. Your monthly payment is

        If you pay this amount each month your mortgage will be paid off in 25 years (or 300 months). Using a spreadsheet and "trial and error," you can see that you need to make additional payments of $215 to pay the mortgage off 5 years earlier.

      2. By making the regular monthly payments, you would pay

        With the additional payment of $215 per month, you will pay

        So, you will save

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               _    _      _____    ______            
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     |    \\  | || | ||   \___ \\   -| ||-   |    \\  
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     |  __//   \____//   /____//   /_____//  |  __//  
     |_|`-`     `---`   `-----`    `-----`   |_|`-`   
     `-`                                     `-`      
    
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  • 10. Amortization Schedules

    Use a spreadsheet. (See Example 3.)

    You take out a home mortgage for $190,000 for 20 years at 5%.

    1. What is the least amount, to the nearest dollar, that you need to pay in addition to the regular payment to pay off the mortgage 5 years early?
    2. Compare the total interest you pay for the 20-year mortgage to the total interest you pay when you pay off the 20-year mortgage 5 years early.
    3. Compare the total interest you pay for a 15-year mortgage for the same amount and at the same rate to the total interest you pay when you pay off the 20-year mortgage 5 years early.

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      _____     _____     ____      ______   ______   
     /  ___||  |  ___||  |  _ \\   /_   _// |      \\ 
    | // __    | ||__    | |_| ||   -| ||-  |  --  // 
    | \\_\ ||  | ||__    | .  //    _| ||_  |  --  \\ 
     \____//   |_____||  |_|\_\\   /_____// |______// 
      `---`    `-----`   `-` --`   `-----`  `------`  
                                                      
    
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  • 11. Balloon Mortgages

    Use a spreadsheet. (See Example 4.)

    You take out a 5-year balloon mortgage for $150,000. The monthly payment is equal to that of a 15-year mortgage with an annual percentage rate of 5%. Find the balloon payment and the total interest that you pay.

    • Worked-Out Solution

      Your monthly payment is

      Making this monthly payment for 5 years produces the following spreadsheet.

      The balloon payment is $111,835.67. You will pay a total interest of $33,007.07.

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      ____     __   __    _____     _____     _____   
     |  _ \\   \ \\/ //  /  ___||  |  ___||  / ____|| 
     | |_| ||   \ ` //  | // __    | ||__   / //---`' 
     | .  //     | ||   | \\_\ ||  | ||__   \ \\___   
     |_|\_\\     |_||    \____//   |_____||  \_____|| 
     `-` --`     `-`'     `---`    `-----`    `----`  
                                                      
    
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  • 12. Balloon Mortgages

    Use a spreadsheet. (See Example 4.)

    You take out a 7-year balloon mortgage for $120,000. The monthly payment is equal to that of a 30-year mortgage with an annual percentage rate of 5.5%. Find the balloon payment and the total interest that you pay.

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      ____     __   __    _____    __   __    ______  
     |  _ \\   \ \\/ //  / ____||  \ \\/ //  /_   _// 
     | |_| ||   \ ` //  / //---`'   \ ` //   `-| |,-  
     | .  //     | ||   \ \\___      | ||      | ||   
     |_|\_\\     |_||    \_____||    |_||      |_||   
     `-` --`     `-`'     `----`     `-`'      `-`'   
                                                      
    
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