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Math Help - Help Mortgage payment

  1. #1
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    Smile Help Mortgage payment

    Hi!!
    In one of my assignments, we had to figure out monthly mortgage payments.

    I used a calculator because I do know know how to show the work.

    The question was getting a 30year mortgage@ 100,000 with a 6.5% rate. What would be monthly payment. Answer is $632.07

    Next question is using a 7.125% interest rate, answer is $673.72
    Next question is a 15 yr loan, at 6.125%

    My text book does not show a formula but i went online and found one but dont know how to figure it out Im pasting it below. THANKYOU
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  2. #2
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    formula i said I would include

    Im losing my mind!!

    Here is the formula I found, if anyone knows how to work it

    First you must define some variables to make it easier to set up:
    # P = principal, the initial amount of the loan
    # I = the annual interest rate (from 1 to 100 percent)
    # L = length, the length (in years) of the loan, or at least the length over which the loan is amortized.

    The following assumes a typical conventional loan where the interest is compounded monthly. First I will define two more variables to make the calculations easier:
    # J = monthly interest in decimal form = I / (12 x 100)
    # N = number of months over which loan is amortized = L x 12

    Okay now for the big monthly payment (M) formula, it is:

    J
    M = P x ------------------------

    1 - ( 1 + J ) ^ -N

    where 1 is the number one (it does not appear too clearly on some browsers)

    So to calculate it, you would first calculate 1 + J then take that to the -N (minus N) power, subtract that from the number 1. Now take the inverse of that (if you have a 1/X button on your calculator push that). Then multiply the result times J and then times P. Sorry, for the long way of explaining it, but I just wanted to be clear for everybody.

    The one-liner for a program would be (adjust for your favorite language):
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  3. #3
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    Lexington, MA (USA)
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    Hello, crazykitty!

    Sorry, I don't understand that formula you found.

    This is an Amortization problem.
    This is the standard formula: . A \;=\;P\cdot\frac{i(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}


    The question was getting a 30-year mortgage for $100,000 with a 6.5% rate.
    What would be monthly payment?
    Answer: $632.07
    We have: . P \:=\: \$100,000,\quad i \:=\: \frac{0.065}{12}\:\approx\:0.0054167\,\quad n \:=\: 360

    Then: . A \;=\;\$100,000\cdot\frac{0.0054167\,(1.0054167)^{3  60}}{(1.0054167)^{360} - 1} \;=\;632.070... \;\approx\;\$632.07




    Next question is using a 7.125% interest rate.
    Answer: $673.72
    We have: . P \:=\:\$100,000,\quad i \:=\:\frac{0.7124}{12}\:=\:0.0059375,\quad n \:=\:360

    Then: . A \;=\;\$100,000\cdot\frac{0.0059375\,(1.0059375)^{3  60} } {(1.0059375)^{360} - 1} \;=\;673.718... \;\approx\;\$673.72




    Next question is a 15 yr loan, at 6.125%
    We have: . P \:=\:\$100,000,\quad i \:=\:\frac{0.06125}{12} \:\approx\:0.005104,\quad n \:=\:180

    Then: . A \;=\;\$100,000\cdot\frac{0.005104\,(1.005104)^{180  }}{(1.005104)^{180}-1} \;=\;850.641... \;\approx\;\$850.64

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  4. #4
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    Hey!

    THANKYOU SO MUCH!!! : )


    I dont know how to thank you all!!! This forum !!!
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