From: "Joe Kelleher" 
Newsgroups: uk.finance
Subject: Re: Calculating mortgage payments
Date: Fri, 24 Feb 2006 21:57:22 -0000

Ronald Raygun wrote:

> [...] Another method assumes (correctly) that you are borrowing the whole
> £100k only for a month, and are then maing an interest payment of £500
> plus an amount to reduce the balance, and are then borrowing slightly
> less than £100k for month 2, etc.  The monthly interest rate is taken
> to be a twelfth of the quoted annual rate.  In other words, the
> monthly payments are  £100k*0.005 / (1 - 1.005^-240)  if the loan is
> to be paid off over the same period, i.e. 240 months.
>
> I would say this second method is more popular these days.  It means
> you pay slightly less each month than with the first.

Thanks for providing such a detailed explanation, including the examples. 
This method appears to be the one used by the mortgage calculators on the 
Nationwide and Guardian.co.uk web sites, so I'm happy with it. The 
derivation of the formula isn't immediately obvious to me, but it agrees 
exactly with a quick spreadsheet I knocked up based on your description, on 
which I used the Goal Seek tool to find the monthly repayment which 
completely repayed the debt in the final month.

>> If repayments were made only once a month,
>
> Only?  It's extremely unusual to make repayments more often than
> monthly.

In fact here is where my confusion lay. I was wrongly assuming the quoted 
interest rate should be continuously compounded throughout the course of 
each month, e.g. as described at 
http://en.wikipedia.org/wiki/Interest#Mathematics_of_interest_rates , 
thereby making the monthly repayments slightly higher than they would 
otherwise be. However, it appears not, and even if it were, the difference 
is only on the order of £1 / month for the examples I considered.


Joe