Mortgage rate mathematics

Colin Green · 2004-11-07T00:27:41+00:00

Hi, I've been trying to figure out the precise maths behind my mortgage interest payments and have discovered that it's not quite what I thought it would be, so I thought I'd share my findings here. Right now I'm with Intelligent Finance's offset mortgage which has an interest rate of 5.95% and which according to IF works out as an APR of 6.1%, see I have always [mistakenly] assumed this difference to be due to an averged out cost of additional fees, the arrangement fee being the most notable. This however is not the case, during a normal mid-term year where the only payments made are interest and repayments, the interest payments appear to be based around 6.1% p/a, not 5.95%. This difference comes about due to the slightly odd way that the interest payments are calculated... IF state that the interest owed is calculated on a daily basis, so you might expect there to be a daily interest rate based on the 5.95% p/a figure right? Well yes and no, the obvious (and correct) way to do this is to take the 365th root of 1.0595 (or 366th on a leap year): daily rate = (1.0595^(1/365))-1 = 0.00482804... etc = 0.482804% / day Thus, if you had a £100,000 mortgage on Jan 1st and applied 0.48% interest per day to the accumulated amount, then on jan 1st the following year you will owe precisely £105,950 - assuming you didn't make any payments all year. Alternatively, to overcome the variable number of days in a month and year you could use the same technique to work out a monthly interest rate, and then go on to work out the daily rate for each month individually. This will have the same result as above, £105,950 of debt at the end of the year. This however is not what happens, with IF you will in fact owe somewhere in the regios of £106,100 and any fees are in addition to this amount. So how does this difference occur? I don't have hard facts to hand but 6.1% is consistent with an alternative scheme of calculating...

Nov 07, 2004 20 Replies

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john boyle 21 years ago

I wouldnt say that too loud, otherwise the Govt Nanny Police, together with Messrs A Robinson and E Rantzen, all armed with 'best by' detectors, will be arresting you shortly.

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Mortgage rate mathematics

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