Calculating Monthly Payment on a Loan

Date: 03/22/2005 at 12:35:01
From: Gameel
Subject: Amortization

I am trying to figure out the math behind amortization tables, 
specifically how you come to the "fixed" monthly payment that
encompasses varying amounts of the interest and principal.  It's easy
to figure out the interest part, but how do you figure out the
principal amount that will create the "fixed" monthly payment that
will reduce the loan to zero at the end of the term?

Date: 03/23/2005 at 23:18:24
From: Doctor Wilko
Subject: Re: Amortization

Hi Gameel,

Thanks for writing to Dr. Math!

The monthly payment can be found by using the following formula:

  P = (Pv*R) / [1 - (1 + R)^(-n)] 
 
where

  Pv  = Present Value (beginning value or amount of loan)
  APR = Annual Percentage Rate (one year time period)
  R   = Periodic Interest Rate = APR/ # of interest periods per year
  P   = Monthly Payment
  n   = # of interest periods for overall time period (i.e., interest
        periods per year * number of years)

If you're familiar with Excel, you can also use the PMT function to
get the monthly payment.

Does this help?  Please write back if you have further questions.

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

Date: 03/24/2005 at 05:34:48
From: Gameel
Subject: Thank you (Amortization)

Dr Wilko:

Thank you very much for responding to my question.  That's the formula
I was looking for!

Gameel