Calculating Adjustable Rate Mortgages

Date: 04/25/2002 at 08:31:59
From: Blair Dudley
Subject: How to calculate adjustable rate mortgages

I see much information on your site about calculating loans with fixed 
terms, but am unable to find anything about how mortgage payments are 
calculated when the term is variable. For instance, if I am applying 
for a loan of $200,000 with the rate of 5.875 using a 3/1 ARM 
(adjustable rate mortgage), how do I calculate the payment? 

Additionally, what will be owing on the loan at the close of the 
three-year term? 

Thanks for the help and I thoroughly enjoy the content of your page.

Date: 04/25/2002 at 10:19:06
From: Doctor Mitteldorf
Subject: Re: How to calculate adjustable rate mortgages

Dear Blair,

Usually your initial payment amount is calculated based on the fiction 
that the loan will continue for 30 years with the same rate. In the 
case you describe, I'd guess the monthly payment would be figured at 
1,183.08. At the end of 3 years, you would owe 191,994 (immediately 
after having made your 36th payment), and that amount would be 
re-amortized in a 27-year mortgage at a new rate. The re-amortization 
would be repeated each year thereafter.

I've written a financial calculator that includes a screen for doing 
simple loans, from which the above numbers were taken. Another screen 
will allow you to play out possibilities for the adjustable rate and 
display amortization tables in which the rate changes in any way you 
specify. The program, which was once widely distributed as a 
commercial product under the name PerSense, is available for free 
download from my page on the Math Forum site:

   http://mathforum.org/~josh/ 

- Doctor Mitteldorf, The Math Forum
  http://mathforum.org/dr.math/