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Math Help - Amortization help

  1. #1
    Junior Member
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    Amortization help

    If I were to purchase a home for 575,000 at 5 3/4% for 30 years, what would my payments be? What would the interst amount per month and the principal amount.
    Any ideas on how I would enter this into am Excel spreadsheet?

    Thanks.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Suwanee View Post
    If I were to purchase a home for 575,000 at 5 3/4% for 30 years, what would my payments be? What would the interst amount per month and the principal amount.
    Any ideas on how I would enter this into am Excel spreadsheet?

    Thanks.
    I expect there is some potted formula for theis, but we can also work it out
    from first principles.

    Let the principal be P = \$ 575000 and \rho = 1+0.0575/12 = 1.004792 be one more than the monthly interest rate, and the monthly repayment be a.

    Then after 1 month our outstanding debt is:

    <br />
D(1) = \rho P - a<br />

    after 2 months:

    <br />
D(2) = \rho (\rho P - a)-a = \rho^2 P - a(1+\rho)<br />

    and after n months:

    <br />
D(n) = \rho^n P - a(1+\rho + ... + \rho^{n-1})=\rho^n P - a\frac{1-\rho^n}{1-\rho}<br />

    Now 30 years is 360 months and after this time our debt will be zero so:

    <br />
D(360) =\rho^{360} P - a\frac{1-\rho^{360}}{1-\rho} = 0<br />

    or:

    <br />
a = \frac{\rho^{360} P (\rho-1)}{\rho^{360}-1} \approx \$ 3355.69<br />

    RonL
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