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Math Help - Compound Interest

  1. #1
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    Compound Interest

    A person wants to buy a set of upholstery in the value $ 3500,00. To finance it in 4 equal installments without input, each service will cost $ 930,36. If, however, one of them is given as input, the value of other benefits reduced will be for $ 907,67.
    The monthly rate of compound interest used in this funding is:

    a) 0,50%
    b) 1,00%
    c) 1,50%
    d) 2,00%
    e) 2,50%
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  2. #2
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    Quote Originally Posted by Apprentice123 View Post
    A person wants to buy a set of upholstery in the value $ 3500,00. To finance it in 4 equal installments without input, each service will cost $ 930,36. If, however, one of them is given as input, the value of other benefits reduced will be for $ 907,67.
    I'm thinking you'll have to translate that to English.

    What does this mean:

    1) "without input"
    2) "each service"
    3) "one of them is given as input"
    4) "other benefits"

    benefits = service = installment = payment or deposit?
    input = down payment?

    Is that exactly how the question is worded? Is this the original language? Perhaps a quick example or two would clear it up. Show how to calculate one payment at the end of the year with and without inputs. Include the language that would describe the situation.

    I might rephrase the question in this manner:

    A person wants to buy a set of upholstery valued at $3500,00. To finance the purchase in 4 equal MONTHLY installments without a downpayment, each INSTALLMENT will be $930,36. If, however, one of the INSTALLMENTS is given as a DOWNPAYMENT, the four MONTHLY INSTALLMENTS are reduced to $ 907,67.

    I might rephrase this way, as well.

    A person wants to buy a set of upholstery valued at $3500,00. To finance the purchase in 4 equal MONTHLY installments without a downpayment, each INSTALLMENT will be $930,36. Just in case you can't calculate an annuity immediate, here is the same problem as an annuity due. If one of the INSTALLMENTS is given as A DOWNPAYMENT, the four MONTHLY INSTALLMENTS are reduced to $907,67.

    I get "e" working as Immediate or as Due. I am a little puzzled why both were give as if all the information were needed. Either one will do.

    Really, the problem statement does NOT define the frequency of payments. There is a HINT as the question asks for "monthly rate", but this is not good enough. Please ask the problem's author to step it up a bit. This is a poorly prepared problem statement even without the translation difficulties.
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  3. #3
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    The correct is

    A person wants to buy a set of upholstery valued at $3500,00. To finance the purchase in 4 equal MONTHLY installments without a downpayment, each INSTALLMENT will be $930,36. If, however, one of the INSTALLMENTS is given as a DOWNPAYMENT, the four MONTHLY INSTALLMENTS are reduced to $ 907,67.

    The monthly rate of compound interest is:

    a) 0,50%
    b) 1,00%
    c) 1,50%
    d) 2,00%
    e) 2,50%
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  4. #4
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    ...or the second.

    What is your plan for solving? It's four payments.

    Without Down Payment

    930,36(v + v^2 + v^3 + v^4) = 3500

    With Down Payment

    907,67(1 + v + v^2 + v^3) = 3500

    Same thing.
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  5. #5
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    Quote Originally Posted by Apprentice123 View Post
    The correct is

    A person wants to buy a set of upholstery valued at $3500,00. To finance the purchase in 4 equal MONTHLY installments without a downpayment, each INSTALLMENT will be $930,36. If, however, one of the INSTALLMENTS is given as a DOWNPAYMENT, the four MONTHLY INSTALLMENTS are reduced to $ 907,67.
    The monthly rate of compound interest is:
    a) 0,50%
    b) 1,00%
    c) 1,50%
    d) 2,00%
    e) 2,50%
    If you only want the answer,
    then use a spread sheet & detemine the results for all 5 interest rates. (You can do this with a calculator in a few minutes.)

    Try this:

    i= 1+ InterestRate/100
    select a rate:

    i = 1.005
    i = 1.010
    i = 1.015
    i = 1.020
    i = 1.025

    Then


    1st payment:
    $3500 * 1.005 = $3517.50
    $3517.50 - $930.36 = $2587.14 amount remaining

    2nd payment:
    $2587.14 * 1.005 = $2600.008
    $2600.08 - $930.36 = $1669.72 amount remaining


    3rd payment:
    $1669.72 * 1.005 = $1678.06
    $1678.06 - $930.36 = $747.70 amount remaining


    Last payment:
    $747.70 * 1.005 = $751.44
    $751.44 - $930.36 = -$178.92 (amount overpaid)

    Thus 1/2% per month is NOT the interest rate used.

    You have only 4 other interest rates. It's easy enough to plug in the different rate & solve.

    However, for questions that might deal with years, you would want to use the sum of a geometric series (as TKHunny as indicated) to get the result.

    Does that help?
    .
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