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6.1 Introduction to Lending

6.1 Introduction to Lending
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  • 13. Pawn Shops

    A pawn shop charges simple interest at an annual percentage rate of 40%. Complete the table showing the interest for various terms and principals. (See Example 5.)

    • Worked-Out Solution

      It is convenient to use a spreadsheet to organize the table.

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     _    _      ___      ______     ___      _____   
    | \  / ||   / _ \\   /_____//   / _ \\   / ____|| 
    |  \/  ||  / //\ \\  `____ `   | / \ || / //---`' 
    | .  . || |  ___  || /___//    | \_/ || \ \\___   
    |_|\/|_|| |_||  |_|| `__ `      \___//   \_____|| 
    `-`  `-`  `-`   `-`  /_//       `---`     `----`  
                         `-`                          
    
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  • 14. Pawning a Gold Ring

    A pawn shop charges simple interest at an annual percentage rate of 40%. You pawn a gold ring and receive a 120-day loan for $500. What is the interest for the loan? (See Example 5.)

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     _    _     ______    ______    ______  __    __  
    | || | ||  /_   _//  /_   _//  /_   _// \ \\ / // 
    | || | ||   -| ||-   `-| |,-    -| ||-   \ \/ //  
    | \\_/ ||   _| ||_     | ||     _| ||_    \  //   
     \____//   /_____//    |_||    /_____//    \//    
      `---`    `-----`     `-`'    `-----`      `     
                                                      
    
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  • 15. Pawning a Television

    A pawn shop charges simple interest at an annual percentage rate of 40%. You pawn a television and receive a 30-day loan for 40% of the $500 resale value. What is the interest for the loan? (See Example 5.)

    • Worked-Out Solution

      The amount of the loan is

      The interest on the loan is

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       _____    _____   __    __   _    _     _____   
      / ___//  |  ___|| \ \\ / // | || | ||  /  ___|| 
      \___ \\  | ||__    \ \/ //  | || | || | // __   
      /    //  | ||__     \  //   | \\_/ || | \\_\ || 
     /____//   |_____||    \//     \____//   \____//  
    `-----`    `-----`      `       `---`     `---`   
                                                      
    
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  • 16. Pawning a Motorcycle

    A pawn shop charges simple interest at an annual percentage rate of 40%. You pawn a motorcycle and receive a 180-day loan for 60% of the $2000 resale value. What is the total amount due? (See Example 5.)

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      _  _     _____     ______    _____    _    _   
     | \| ||  |  ___||  /_____//  |  ___|| | |  | || 
     |  ' ||  | ||__    `____ `   | ||__   | |/\| || 
     | .  ||  | ||__    /___//    | ||__   |  /\  || 
     |_|\_||  |_____||  `__ `     |_____|| |_// \_|| 
     `-` -`   `-----`   /_//      `-----`  `-`   `-` 
                        `-`                          
    
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  • 17. Service Charges

    A pawn shop includes a service charge according to the table. You pay $5.59 in interest on a 60-day loan for $85. Find (a) the annual percentage rate for only the interest and (b) the annual percentage rate including the service charge. (See Example 6.)

    • Worked-Out Solution

      a. The annual percentage rate for the interest only is

      b. The annual percentage rate including the service charge is

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     _____      ______   __   _    __   __    _____   
    |  __ \\   /_   _// | || | ||  \ \\/ //  /  ___|| 
    | |  \ ||   -| ||-  | '--' ||   \ ` //  | // __   
    | |__/ ||   _| ||_  | .--. ||    | ||   | \\_\ || 
    |_____//   /_____// |_|| |_||    |_||    \____//  
     -----`    `-----`  `-`  `-`     `-`'     `---`   
                                                      
    
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  • 18. Service Charges

    A pawn shop includes a service charge according to the table. You pay $336 in interest on a 1-year loan for $700. Find (a) the annual percentage rate for only the interest and (b) the annual percentage rate including the service charge. (See Example 6.)

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      ______   __   __  __    __    _____             
     /_   _//  \ \\/ // \ \\ / //  |  ___||     ___   
     `-| |,-    \ ` //   \ \/ //   | ||__      /   || 
       | ||      | ||     \  //    | ||__     | [] || 
       |_||      |_||      \//     |_____||    \__ || 
       `-`'      `-`'       `      `-----`      -|_|| 
                                                 `-`  
    
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  • 19. Service Charges

    A pawn shop includes a service charge according to the table. You pay $10.48 in interest on a 45-day loan for $340. Find (a) the annual percentage rate for only the interest and (b) the annual percentage rate including the service charge. (See Example 6.)

    • Worked-Out Solution

      a. The annual percentage rate for the interest only is

      b. The annual percentage rate including the service charge is

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      _____      ___      ______   _    _    _    _   
     |__  //    / _ \\   /_____// | || | || | |  | || 
       / //    / //\ \\  `____ `  | || | || | |/\| || 
      / //__  |  ___  || /___//   | \\_/ || |  /\  || 
     /_____|| |_||  |_|| `__ `     \____//  |_// \_|| 
     `-----`  `-`   `-`  /_//       `---`   `-`   `-` 
                         `-`                          
    
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  • 20. Reimbursement

    When you do not make your payments and your pawned item sells, you may be entitled to the difference of the selling price and the total amount due. (The total amount due includes expenses incurred by the pawn shop to sell the item.)

    1. You do not repay the loan in Exercise 16, and the pawn shop incurs $60 in expenses to sell the motorcycle. Find the sum of the total amount due and the expenses incurred to sell the motorcycle.
    2. The motorcycle sells for $1700. How much money should you receive
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      _____     ______    _____    __   __    _____   
     / ____||  /_   _//  |__  //   \ \\/ //  /  ___|| 
    / //---`'   -| ||-     / //     \ ` //  | // __   
    \ \\___     _| ||_    / //__     | ||   | \\_\ || 
     \_____||  /_____//  /_____||    |_||    \____//  
      `----`   `-----`   `-----`     `-`'     `---`   
                                                      
    
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