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Math Help - Simple Interest Challenge Problem

  1. #1
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    Simple Interest Challenge Problem

    A father wanted to show his son what it might be like to borrow money from a financial insitution. When his son asked if he could borrow $120 the father lent him the money and setup the following arrangements:
    He charged his son $6 for the loan of $120.
    Therefore the son received $114 and agreed to pay his father 12 installments of $10 a month, beginning one month from today,until the loan was repaid.
    Find the approximate rate of simple interest the father charged on this loan.
    Please show some work
    Thanks a ton!
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  2. #2
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    Re: Simple Interest Challenge Problem

    That looks like a pretty straight forward problem. He received $114 and payed back $120 over 12 months so the total interest was $6 on $114 for one year. What percent is that?
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  3. #3
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    Re: Simple Interest Challenge Problem

    but dont i have to account for the twelve equal payments. wouldnt the $6 dollars interest on $114 (which is 5.3%) be if there was only one payment at the end of 12 months?
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  4. #4
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    Re: Simple Interest Challenge Problem

    Quote Originally Posted by thut View Post
    but dont i have to account for the twelve equal payments. wouldnt the $6 dollars interest on $114 (which is 5.3%) be if there was only one payment at the end of 12 months?
    You're right. Hallsofivy had too much turkey stuffing!
    You're asked to "find the approximate rate of simple interest"; I'd do it this way:
    114/2 = 57 (approximate average owing) : 6/57 = .10526 ; so 10.53 %

    You can be a little more precise by taking the 12 monthly balances: 114, 104, 94....14, 4
    adding 'em up, divide by 12 for average...won't be much of a difference...
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  5. #5
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    Re: Simple Interest Challenge Problem

    Thanks Wilmer! but im a little bit unclear as to why you divide the 114 by 2 to get the approximate average owing?
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  6. #6
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    Re: Simple Interest Challenge Problem

    Quote Originally Posted by thut View Post
    Thanks Wilmer! but im a little bit unclear as to why you divide the 114 by 2 to get the approximate average owing?
    The $114 is owing at beginning of year...gradually reduces to zero OVER A YEAR: so approximately half is
    owing on average.
    Take a simpler case: 300, reducing by 100:
    300
    200
    100
    ===
    600
    600 / 3 = 200 average
    Thanks from thut
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  7. #7
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    Re: Simple Interest Challenge Problem

    okay thanks Wilmer! I understand it now.
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  8. #8
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    Re: Simple Interest Challenge Problem

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