nishri@utcs.UUCP (Alex Nishri) (11/06/84)
I have seen several programs which calculate monthly mortgage payments based on the mortgage amount, its duration and the percentage interest rate. However, all of these programs appear to use formulas which apparently are valid only for American mortgages. Does anyone know what the difference is in the Canadian way of calculating mortgages? What are the correct formulas to use? (I asked at the bank and they told me they didn't know how to calculate mortgages -- they just use printed tables!)
milan@hcrvax.UUCP (Milan Strnad) (11/06/84)
Banks don't know how to calculate mortgages? They only use printed tables... That reminds me of an episode of "Yes, Minister", a British political comedy shown on channel 19 -- a banker was looking around for a job. When asked what he knew, he stated, "I don't know anything -- I'm a banker." Quite appropriate here. milan (..hcr!hcrvax!milan)
clarke@utcs.UUCP (Jim Clarke) (11/07/84)
I wrote a small Fortran (!) program about nine years ago to calculate my in-laws' mortgage. Before doing so, I looked up a set of tables that were published in Canada and made specific reference to (as I recall) Ontario's regulations. There was certainly no reference to the number of days in each month or in the year; that must be a frill added since computing got cheaper. This book -- published around 1959, I think -- made a point of showing how to calculate anyone's mortgage payments by hand from the general cases tabulated. (It certainly did not make a point of showing the formulas used, and I had to do a fair amount of cogitation and experimentation. After a while I did manage to duplicate a table I had for a particular mortgage as well.) Conclusion: things have changed in mortgage calculation, and you probably have to check details carefully to reproduce a particular bank's tables.
kpmartin@watmath.UUCP (Kevin Martin) (11/08/84)
>Does anyone know what the difference is in the Canadian way >of calculating mortgages? What are the correct formulas to use? I think I remember a difference in the relation between the actual monthly rate and the quoted annual rate: One calculation is: monthly_rate = annual_rate / 12 Since interest is compounded monthly, this means that the interest over a year (if no payments were made) would actually exceed principal*annual_rate. The other calculation is: monthly_rate = 12th root of (1 + annual_rate) - 1 which, when compounded monthly, gives the correct actual annual rate. e.g. for a 12% quoted annual rate, one calculation gives 1% monthly, the other gives 0.95% monthly. The 'actual' interest paid annually using the first calculation is 12.68%. On a $50000 principal, this makes a $25 per month difference. Unfortunately, I don't remember which is the US way. You can compensate for this difference when using a mortgage program by fudging the interest rate you tell it to use.
jmsellens@watmath.UUCP (John M Sellens) (11/08/84)
Well, maybe I can clarify Kevin's comments a little bit. The compounding period and the frequency of the payments do not necessarily coincide. For example, most mortgages are paid monthly, but the interest is compounded semi-annually. Using Kevin's example of a 12% nominal annual rate, the monthly rate when interest is compounded monthly is 1% (12% divided by 12 months). If compounded annually, the monthly rate is 0.95% (the twelfth root of 1.12 minus 1). If the interest was compounded semi-annually, the monthly rate is the sixth root (since there are 6 months or periods in the compounding period) of 1 plus half of the nominal annual rate (since there are two compouding periods in a year) minus 1 0.98% = sixth root of 1.06 - 1 Now - the original question - the difference between the Canadian and American methods. The Americans generally treat things as if each month had 30 days, and each year has 12 months of 30 days each for a total of 360 days. Canadians take a more realistic view of things. Now, depending on how you calculate things, this may or may not affect your results. Remember that the important thing is always the effective annual rate - the more frequently the interest is compounded, the higher the effective annual rate (for a given nominal annual rate). John