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6.1 Introduction to Lending

6.1 Introduction to Lending
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  • 21. Ordinary Simple Interest

    You borrow $4200 from a relative on January 5, 2012, to buy solar panels for your roof and windows with insulated glazing. The annual percentage rate is 8.9%. You agree to repay the loan on May 25, 2012.

    Simple interest based on a 360-day year in which each month has 30 days is called ordinary simple interest. When using ordinary simple interest, you can use the formula below to find the number of days in a term from a month M, day D, and year Y to a later month m, day d, and year y. (Note: January = 1, February = 2, etc.)

    1. Use the formula to find the number of days in the term.
    2. Find the total amount due using ordinary simple interest.
    • Worked-Out Solution

      a. In the formula, January =1 and May = 5.

      b. The interest is

      So, the total amount due is

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       _____     ___      ______   __   __   _____    
      / ___//   / _ \\   /_   _//  \ \\/ // |  __ \\  
      \___ \\  / //\ \\  `-| |,-    \ ` //  | |  \ || 
      /    // |  ___  ||   | ||      | ||   | |__/ || 
     /____//  |_||  |_||   |_||      |_||   |_____//  
    `-----`   `-`   `-`    `-`'      `-`'    -----`   
                                                      
    
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  • 22. Exact Simple Interest

    You borrow $4200 from a relative on January 5, 2012, to buy solar panels for your roof and windows with insulated glazing. The annual percentage rate is 8.9%. You agree to repay the loan on May 25, 2012.

    What is the actual number of days in the term? Find the total amount due using exact simple interest, as on page 256.

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      ______   __   __  __    __    _____     _  _   
     /_____//  \ \\/ // \ \\ / //  |  ___||  | \| || 
     `____ `    \ ` //   \ \/ //   | ||__    |  ' || 
     /___//      | ||     \  //    | ||__    | .  || 
     `__ `       |_||      \//     |_____||  |_|\_|| 
     /_//        `-`'       `      `-----`   `-` -`  
     `-`                                             
    
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  • 23. Comparing Simple Interests

    Simple interest based on a 360-day year in which each month has 30 days is called ordinary simple interest. When using ordinary simple interest, you can use the formula below to find the number of days in a term from month M, day D, year Y to a later month m, day d, and year y. (Note: January = 1, February = 2, etc.)


    Which type of interest costs you more money? Will this always be true? Explain.

    • Worked-Out Solution

      To determine which type of interest costs more, you can use a spreadsheet.

      For simplicity, use a principal of $1000 and an annual interest rate of 10%. Notice that the formula for ordinary interest yields slightly more interest than the formula for simple interest. This is true until the end of the year, when both formulas yield the same amount of interest.

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               __   __    _____      ___     __   _   
        ___    \ \\/ //  /  ___||   / _ \\  | || | || 
       /   ||   \ ` //  | // __    / //\ \\ | '--' || 
      | [] ||    | ||   | \\_\ || |  ___  ||| .--. || 
       \__ ||    |_||    \____//  |_||  |_|||_|| |_|| 
        -|_||    `-`'     `---`   `-`   `-` `-`  `-`  
         `-`                                          
    
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  • 24. Comparing Simple Interests

    Do you think it is appropriate to use ordinary simple interest as an approximation of exact simple interest? Explain.

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     _____     _    _     ______     ___     _____    
    |  __ \\  | || | ||  /_   _//   / _ \\  |  __ \\  
    | |  \ || | || | ||  `-| |,-   / //\ \\ | |  \ || 
    | |__/ || | \\_/ ||    | ||   |  ___  ||| |__/ || 
    |_____//   \____//     |_||   |_||  |_|||_____//  
     -----`     `---`      `-`'   `-`   `-`  -----`   
                                                      
    
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  • 25. Banker's Rule

    The Banker's Rule is another type of simple interest that is similar to ordinary simple interest. It is based on a 360-day year, but you use the actual number of days in the term when calculating interest. Does this benefit the lender or the borrower? Explain.

    • Worked-Out Solution

      To determine who benefits more, you can use a spreadsheet.

      For simplicity, use a principal of $1000 and an annual interest rate of 10%. Notice that the formula using Banker's Rule yields slightly more interest than the formula for simple interest. So, the lender benefits more.

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      ______    _____    _    _     ______    ______  
     /_____//  |  ___|| | || | ||  /_   _//  /_____// 
     `____ `   | ||__   | || | ||   -| ||-   `____ `  
     /___//    | ||__   | \\_/ ||   _| ||_   /___//   
     `__ `     |_____||  \____//   /_____//  `__ `    
     /_//      `-----`    `---`    `-----`   /_//     
     `-`                                     `-`      
    
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  • 26. Loan Options

    You have 3 loan options for borrowing $2500. You will repay the simple interest loan in 180 days.

    1. Find the interest for each loan.
    2. Find the annual percentage rate of each loan, including the service charge.
    3. Find the total amount due for each loan.
    4. Which loan would you choose? Explain
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      ______     ___       _____     ___      _____   
     /_   _//   / _ \\    / ___//   / _ \\   |__  //  
       | ||    | / \ ||   \___ \\  | / \ ||    / //   
      _| ||    | \_/ ||   /    //  | \_/ ||   / //__  
     /__//      \___//   /____//    \___//   /_____|| 
     `--`       `---`   `-----`     `---`    `-----`  
                                                      
    
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