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Math Help - Annuity problem

  1. #1
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    Joined
    Sep 2005
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    10

    Annuity problem

    You can purchase a residential building lot for $60,000 cash, or for $10,000 down and month-end payments of $1000 for five years. If money is worth 7.5% compounded monthly, which option should you choose?

    Answer: Second option is $94.69 cheaper
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  2. #2
    Newbie
    Joined
    Sep 2007
    Posts
    9

    Annuity

    The value of the annuity is X * (1-v^n)/i' where

    i = 7.5%
    i' = 7.5%/12 = 0.625% i.e. the monthly interest rate
    v = (1+i')^-1 = 0.99378882
    X = 1000
    n = 5 * 12 = 60

    Annuity = 1000 * ( 1- 0.99378882^60) / 0.00625 = 49905.31

    Adding the 10000 downpayment gives 59905.31 i.e. a saving of 94.69
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