Ron Larson
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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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