1. ## 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.

2. Originally Posted by Suwanee
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:

$
D(1) = \rho P - a
$

after 2 months:

$
D(2) = \rho (\rho P - a)-a = \rho^2 P - a(1+\rho)
$

and after $n$ months:

$
D(n) = \rho^n P - a(1+\rho + ... + \rho^{n-1})=\rho^n P - a\frac{1-\rho^n}{1-\rho}
$

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

$
D(360) =\rho^{360} P - a\frac{1-\rho^{360}}{1-\rho} = 0
$

or:

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

RonL