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 $\displaystyle P = \$ 575000$ and $\displaystyle \rho = 1+0.0575/12 = 1.004792$ be one more than the monthly interest rate, and the monthly repayment be $\displaystyle a$.
Then after 1 month our outstanding debt is:
$\displaystyle
D(1) = \rho P - a
$
after 2 months:
$\displaystyle
D(2) = \rho (\rho P - a)-a = \rho^2 P - a(1+\rho)
$
and after $\displaystyle n$ months:
$\displaystyle
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:
$\displaystyle
D(360) =\rho^{360} P - a\frac{1-\rho^{360}}{1-\rho} = 0
$
or:
$\displaystyle
a = \frac{\rho^{360} P (\rho-1)}{\rho^{360}-1} \approx \$ 3355.69
$
RonL