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Math Help - geometric sequence

  1. #1
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    geometric sequence

    Charles borrows $6000 for a new car.Compound intrest is charged on the loan at at a rate of 2% per month.Charles has to pay off the loan with 24 equal monthly payments.Calculate the value of each monthly payment.


    Any help is appreciiated the answer in text is 317.226
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  2. #2
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    Re: geometric sequence

    I don't think using geometric sequences here is appropriate, as you are paying money on the amount owing, instead of interest just accumulating on what is owed. This is actually an annuity. I suggest looking up the annuities formula.
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  3. #3
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    Re: geometric sequence

    Hello, spacemenon!

    Are you expected to solve this with Geometric Sequences?
    That is an awesomely involved problem.


    Charles borrows $6000 for a new car.
    Compound intrest is charged on the loan at at a rate of 2% per month.
    Charles has to pay off the loan with 24 equal monthly payments.
    Calculate the value of each monthly payment.

    Textbook answer: 317.226 . ??

    That is a strange answer.
    First of all, it should be rounded to the nearest cent.
    Second, it is inaccurate.


    This is an Amortization problem.

    Formula: . A \;=\;P\frac{1(1+i)^n}{(1+i)^n-1}

    . . where: . \begin{Bmatrix}A &=& \text{periodic payment} \\ P &=& \text{principal borrowed} \\ i &=& \text{periodic interest rate} \\ n &=& \text{number of periods} \end{Bmatrix}


    We have: . P = 6000,\;i = 0.02,\;n = 24

    Hence: . A \;=\;6000\,\frac{0.02(1.02)^{24}}{1.02^{24}-1} \;=\;317.2265835 \;\;{\color{blue}\approx\;317.227}

    Therefore: . A \;=\;\$317,23
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  4. #4
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    Re: geometric sequence

    you r right i gave the calculater answer text answer is 317.23
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