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```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
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

http://mathforum.org/~josh/

- Doctor Mitteldorf, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Interest

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