Conference kaosws::canada

    
    OK, here you go ...  hope it makes sense
    
    
    
    Where I is the Quoted interest rate
          I1 is the Interest rate for the compounding period
    	  M is the Payment
    	  P is the Principal
          Z is the Amortization in whatever units (Months, weeks,
                   biweeks,semimonths etc)
    	  X is the number of compounding period per 6 months (6 for months
    		13 for bi weeks, 26 for weeks, 12 for semi-months)
    
    	IS = I/2
        I1 = (1+IS^(1/X))-1
    
        M = P*I1*(1+I)^Z / ((1+I1)^Z)-1)
    
    Examples 
    
    
    1)	$100,000  paid monthly  25 year amortization 12% rate
    
    	I = .12		( 12% )
    	P = 100000	( $100,000 )
    	X = 6		( Interest Rate Calculated Semi-annually )
    	Z = 300		( 25 years = 25*12 = 300 months amortization )
    
    	IS = .06
    	I1 = .00975883
    
    	M = 1031.90
    	
        Monthly payment = $1,031.90
    
    2)	$100,000 12% weekly pay 25 years
    
    	X = 26
    	Z = 52 * 25 = 1300
    
    	M = 237.24
    
    	Weekly payment 237.24
    
    $100,000 12% weekly pay 17.5 years
    
    	X = 26
    	Z = 52 * 17.5
    
    	M = 257.92
    
    	Weekly payment 257.92  (note this is approx 1 month divided by 4
    
    ---------------------------------------------------------------
    
    For Monthly and semimonthly payments, the result you get from this
    formula is exact.  For weekly and bi-weekly payments, this yields
    very close to the correct amount, because it does not take into
    account that there are more than 52 weeks a year.  The result though
    is usually less than $1 different.
    
    Also, it does not take into account the fact that the months are
    varying length.  Generally most financial institutions used to assume
    that the months are all an equal length ... but now some are taking
    the differences into account, either by adjusting the payment, or 
    usually by shortening the amortization a little bit extra each year.
    (Over the life of the mortgage though this is only a matter of a few
    weeks).
    
    Note that some institutions quote rates for weekly, biweekly and semi-
    monthly that are calculated as 1/4, 1/2 and 1/2 the monthly payments
    respectively.  These all have the effect of reducing the amortization
    period.  For example a 25 year mortgage paid weekly as 1/4 of the
    monthly payments is really approximately a 17.5 year amortization.  (If
    you use the above formula with an amortization of 17.5 years and weekly
    payments, you'll find the payments very similar to dividing the monthly
    payment by 4)
    
    
    
    I have a program that will calculate the amounts and also an
    amortization program for Canadian Mortgages if you are interested.
    (The latter has a few tweaks to do to it)
    
    Stuart

    There's a program in the metoo""::sw_tools_catalog for calculating
    stuff for mortgages - don't remember the exact note number but a
    dir/title=mortgage should get it.
    
    I have used it to give me and idea what payments could be like
    especially with the current downward trend in rates.
    
    	Owen
    

    The mortgage program in the tools catalogue is for calculating
    mortgages the *American* way, where the interest rate is "Calculated
    monthly" as opposed to the Canadian way which is "Calculated Semi-
    annually).
    
    The difference, for example, on a monthly pay mortgage quoted as
    12% per year, on an American mortgage, you'll be charged 1% interest
    per month.  On a Canadian mortgage, you'll be charged 0.976% interest
    per month.  It results in Canadian payments being slightly lower.
    
    If you use the American program, you'll forever be having disagreements
    with the bank / trust company!
    
    Stuart

    Well thanks for the info, as soon as I get some time I'll give these
    things a try.
    
    Then again, now that 'we' have Lotus in All-in-1, someone could just
    mail me a spreadsheet already done, and I could just try it...
    
    

    All-in-1 is slow to access from here, and setting up Macros in
    123 is a pain ...
    
    Stuart

    I have a "C" program that I created to show mortgage payments.
    It's not too fancy, it doesnt give a table for the life of the 
    mortgage or anything. It does show the payment on monthly and weekly
    or bi-weekly payments. It also shows the amount remaining on your
    mortgage after so many payments.
    
    It works for my mortgage, you are free to try it for yours. Just 
    send me mail and I'll send you the source code.

From:	KAOFS::CSC32::S_BROOK      "I just passed myself going the other way"  7-JUN-1993 12:32:07.00
To:	KAOFS::TROOA::BOUNDY
CC:	S_BROOK
Subj:	RE: KAOSWS::CANADA note 600.1

Hi Graham,

>Try as I might, I can't get the mortgage calculation to work. Specifically,
>
>        M = P*I1*(1+I)^Z / ((1+I1)^Z)-1)

Oops ... there is one bug ... that should be (1+I1) on top

Stuart
    

    Stuart, thanks for the Canadian mortgage payment formula.  Now, do you,
    or anyone else, have the formula for calculating the interest component
    of each payment?
    
    Lockyer

I'm willing to bet he does...

/Mario

Yup, sure do!

Note that this has to be recalculated each month on the declining 
Principle balance ...

Where

INT= monthly interest payment
I= interest rate per annum (expressed as decimal ... eg 12% =.12)
P= outstanding Principle
IM= monthly interest rate (as a decimal)


IM = ((I/2)+1)^(1/6))-1

INT = P * IM

So, for example

Where I = 10% p.a.  Outstanding balance = $100,000.00

IM = (1.05^.16666666667)-1
   = .0081648460519 etc .....

INT = $816.48

    Thanks Stuart, but I dod have a question -
    
    Is this formula valid for all payment frequencies (ie. for monthly,
    bi-weekly, weekly and semi-monthy)?
    
    Regards,
    
    Garry
    

Where
    INT= periodic interest payment
    I= interest rate per annum (expressed as decimal ... eg 12% =.12)
    P= outstanding Principle
    IM= periodic interest rate (as a decimal)
    
    For Semi Monthly ...
    
    IM = ((I/2)+1)^(1/12))-1
    
    
    For Bi-Weekly
    
    IM = ((I/2)+1)^(1/13))-1
    
    
    For Weekly
    
    IM = ((I/2)+1)^(1/26))-1
    
    
    Then INT = IM * P
    
    
    This works for Canadian Mortgage Payments where the Interest
    rate is quoted in the following manner for example 
    
    10% calculated semi-annually, not in advance
    
    and compounded at the rate of payment frequency.
    
    NOTE that there are SOME lenders who still compound monthly with
    higher payment frequencies and make some kind of interest rate
    adjustment to cope with your higher payment frequency.  This would
    be explained in the disclosure statements from the lender.
    
    

    Thanks again,
    
    Garry