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Thread: Help Please!

  1. #1
    Oct 2008

    Help Please!

    Hello all, need some help on a problem. Hoping somone can lend a hand.

    Brandi Just bought a house for 249,500.00. She paid 25,000.00 down and took a 30 year mortgage on the balance. The bank is charging her 7.25% interest. What will be her monthly payment on the mortgage?

    Am I right in using...

    P(1+r/n)^nt = R((1+r/n)^nt divided by r/n)?

    If so... im clueless as to where to plug anything in.

    Any assistance will be a awesome.

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  2. #2
    MHF Contributor
    Aug 2007
    I just cannot adequately stress the concept of "Basic Principles". Just a little familiarity with basic algebra and you NEVER - EVER have to worry about which formula to use. Why would you not want that?!

    Catalogue of what we know:

    Value = 249500
    Down Payment = 25000
    Amount Financed = 249500 - 25000 = 224500
    APR = 7.25%
    Monthly Interest Rate = 7.25%/12 = 0.604166...%

    A few convenient monthly definitions:

    i = 0.006041666....
    v = 1/(1+i)
    R = Amount Financed = 224500
    P = Regular Payment = ?? This is what we seek.
    n = 12*30 = 360 = Number of Months Financed

    Having said that, the whole thing is written easily.

    $\displaystyle R = P(v + v^{2} + v^{3} + ... + v^{n})$

    The only challenge is adding up the stuff in the parentheses. However, this should be a very, very well-known process or derivation that produces:

    $\displaystyle R = P \left(\frac{v-v^{n+1}}{1-v}\right)$

    If you like, a little more algebra puts it in a more standard form, but there really is no need to do this.

    $\displaystyle R = P \left(\frac{v-v^{n+1}}{1-v}\right)\;=\;P \left(\frac{v-v^{n+1}}{i \cdot v}\right)\;=\;P \left(\frac{1-v^{n}}{i}\right)$

    It is hoped that you can now solve for 'P' and answer the demands of the problem statement. And, really, practice doing what you see here. Get good at it. You will remove all future confusion concering which formula to use. Create your own!
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