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Math Help - Nominal and effective interest rates

  1. #1
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    Nominal and effective interest rates

    Problem statement: A loan shark lends someone money saying, "If I lend you $50 on Friday, you owe me the $50 plus an extra $10 on the following Friday." (The lending goes on for a year)

    a) What is the nominal interest rate per year being charged?

    b) What effective interest rate is the loan shark charging?

    c) If the loan shark started with $50, and was able to keep it, and all the money received loaned out at all times, how much does he have at the end of one year?

    Here are my answers:

    a) (10/50)*(365/7) = 10.42 = 1042%

    b) i = e^x-1
    i = e^10.42-1 = 33 522.43 = 3 352 243.42%

    c) I'm not sure how to do c

    My numbers are very large. Is that normal? Please correct me if I'm wrong because these numbers are just outrageous.
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  2. #2
    MHF Contributor
    Joined
    Dec 2007
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    Ottawa, Canada
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    enchanteuse? same as "femme fatale"?

    a) Well, $10 on $50 for a week is obviously 20% per week.
    As simple annual interest: 52 * 20 = 1040%

    b) effective = 1.2^52 - 1 = 13104.63... - 1 = 13103.63...%
    YES: means $1 accumilates to ~$13,104 over 1 year!

    c) if that means he reinvests the interest at same rate, like a week
    after the initial $50, he lends $60 and collects $72 ($12 interest):
    Code:
    week             interest        worth
       0                  0             50
       1                 10             60
       2                 12             72 
    .....
      51              91004         546026
      52             109206         655232
    YES: that's 655,232 bucks
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