Ron Larson
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6.3 Home Mortgages

6.3 Home Mortgages
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  • 13. Buying Versus Renting

    Compare the costs of buying the home and renting a comparable home for $1600 per month. (See Example 5.)

    You take out a home mortgage for $224,000 for 30 years at 5%. After 5 years, you move to a different state and sell the home for $294,280. Assume that if you did not buy the home, you could have invested the down payment and earned $12,000 in interest.

    • Worked-Out Solution

      Buying: Here is a tally of the amounts you spent and saved by buying.

      Renting: Here is a tally of what you would have spent by renting.

      So, for this particular scenario, it would have cost you a lot less had you rented instead of bought.

      The reason for this is that after 5 years, the home was worth only slightly more than what you paid for it.

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      _  __   __   __   _____      _____    __   __  
 | |/ //  \ \\/ // |  __ \\   |  ___||  \ \\/ // 
 | ' //    \ ` //  | |  \ ||  | ||__     \   //  
 | . \\     | ||   | |__/ ||  | ||__     / . \\  
 |_|\_\\    |_||   |_____//   |_____||  /_//\_\\ 
 `-` --`    `-`'    -----`    `-----`   `-`  --`
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  • 14. Buying Versus Renting

    Compare the costs of buying the home and renting a comparable home for $1600 per month. (See Example 5.)

    You take out a home mortgage for $200,000 for 30 years at 4%. After 6 years, you move to a different city and sell the home for $281,540. Assume that if you did not buy the home, you could have invested the down payment and earned $13,000 in interest.

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                 ___      ______    _____     ____    
    ___     / _ \\   /_____//  |  ___||  |  _ \\  
   /   ||  | / \ ||  `____ `   | ||__    | |_| || 
  | [] ||  | \_/ ||  /___//    | ||__    | .  //  
   \__ ||   \___//   `__ `     |_____||  |_|\_\\  
    -|_||   `---`    /_//      `-----`   `-` --`  
     `-`             `-`
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  • 15. Price to Rent Ratio

    The cost of a home is $162,000. The rent for a comparable home is $800 per month. Find the price-to-rent ratio.

    • Worked-Out Solution

      The price to rent ratio is

      Figuring that a typical price to rent ratio is 15, this ratio is slightly high.

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       _____    _____   __    __     ___     __   _   
  / ___//  |  ___|| \ \\ / //   / _ \\  | || | || 
  \___ \\  | ||__    \ \/ //   | / \ || | '--' || 
  /    //  | ||__     \  //    | \_/ || | .--. || 
 /____//   |_____||    \//      \___//  |_|| |_|| 
`-----`    `-----`      `       `---`   `-`  `-`
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  • 16. Price-to-Rent Ratio

    The cost of the home is $156,000. The rent for a comparable home is $700 per month. Find the price-to-rent ratio.

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      _____     _____              _    _     _  __  
 |__  //   |  ___||   ____    | || | ||  | |/ // 
   / //    | ||__    |    \\  | || | ||  | ' //  
  / //__   | ||__    | [] ||  | \\_/ ||  | . \\  
 /_____||  |_____||  |  __//   \____//   |_|\_\\ 
 `-----`   `-----`   |_|`-`     `---`    `-` --` 
                     `-`
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  • 17. Housing Bubble

    Use the graph on page 279. Suppose home prices followed the pre-bubble trend. (See Example 6.)

      1. What would have been the price of a home in 2006?
      2. How much more was the actual price of a home in 2006?

    • Worked-Out Solution
      1. Had housing prices followed the pre-bubble trend, the average cost of a home in 2006 would have been about $190,000.
      2. With the increase in prices due to the "bubble," the average cost of a home in 2006 was about $245,000. This was an increase of $55,000 more than would have been expected by the linear pattern of growth.
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     _    _    _    _    _    _      ___    __    __  
| || | || | || | || | |  | ||   / _ \\  \ \\ / // 
| || | || | || | || | |/\| ||  / //\ \\  \ \/ //  
| \\_/ || | \\_/ || |  /\  || |  ___  ||  \  //   
 \____//   \____//  |_// \_|| |_||  |_||   \//    
  `---`     `---`   `-`   `-` `-`   `-`     `
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  • 18. Housing Bubble

    Use the graph on page 279 to estimate the percent change in home prices from 2004 to 2010. (See Example 6.)

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      _____    _    _    ______      ___     _    _   
 |__  //  | || | || |      \\   / _ \\  | |  | || 
   / //   | || | || |  --  //  / //\ \\ | |/\| || 
  / //__  | \\_/ || |  --  \\ |  ___  |||  /\  || 
 /_____||  \____//  |______// |_||  |_|||_// \_|| 
 `-----`    `---`   `------`  `-`   `-` `-`   `-`
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  • 19. Housing Bubble

    Use the graph on page 279 to estimate the percent decrease in home prices from 2007 to 2009. (See Example 6.)

    • Worked-Out Solution

      From 2007 to 2009, the median housing price fell from about $248,000 to about $217,000. This is a percent decrease of about

      So, from 2007 the typical value of a house fell by about 13%.

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     _    _    _    _     _  __    ______     _____  
| \  / || | || | ||  | |/ //  /_   _//   / ___// 
|  \/  || | || | ||  | ' //    -| ||-    \___ \\ 
| .  . || | \\_/ ||  | . \\    _| ||_    /    // 
|_|\/|_||  \____//   |_|\_\\  /_____//  /____//  
`-`  `-`    `---`    `-` --`  `-----`  `-----`
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  • 20. Housing Bubble

    Use the graph on page 279 to compare the percent increase in home prices from 1989 to 1998 to the percent increase in home prices from 1998 to 2007. (See Example 6.)

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               _    _     ______   __   __  __    __  
  ____    | || | ||  /_____//  \ \\/ // \ \\ / // 
 |    \\  | || | ||  `____ `    \ ` //   \ \/ //  
 | [] ||  | \\_/ ||  /___//      | ||     \  //   
 |  __//   \____//   `__ `       |_||      \//    
 |_|`-`     `---`    /_//        `-`'       `     
 `-`                 `-`
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