Canadian mortgage payment + accelerated bi-weekly.
Monthly payment
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Bi-weekly
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Accelerated bi-weekly
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Worked example
Take a $500,000 mortgage at 5.5 percent over a 25-year amortization. Canadian fixed mortgages compound semi-annually, not monthly, so the posted 5.5 percent first becomes a semi-annual rate of 2.75 percent and is then converted to an effective monthly rate of about 0.45317 percent. Running the standard amortization formula over 300 monthly payments gives a payment of about $3,051.96. A plain bi-weekly payment is simply the monthly figure times 12 divided by 26, which is $1,408.60 and pays off in the same 25 years. Accelerated bi-weekly instead halves the monthly payment to $1,525.98 and collects it every two weeks, which works out to roughly one extra monthly payment a year and shaves about three to four years off the term.
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How it is calculated
The payment uses the standard annuity formula, payment equals principal times r times (1 plus r) to the power n, divided by (1 plus r) to the power n minus 1, where n is the number of payments and r is the periodic rate. The Canadian twist is the rate conversion: federal law requires fixed mortgage interest to be expressed compounded semi-annually, so the annual rate is halved, then re-expressed as an equivalent monthly rate before the formula runs. Bi-weekly and accelerated bi-weekly are derived from that monthly figure rather than recalculated from scratch. Because accelerated bi-weekly collects half the monthly payment 26 times a year, you make the equivalent of 13 monthly payments instead of 12, and the extra principal compounds into a shorter term and lower total interest.