All the Numbers

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How a mortgage payment is worked out

A mortgage payment is the same amount every month, set so that the balance reaches zero at the end of the amortization. Part of each payment is interest on what is still owed; the rest repays principal. Early payments are mostly interest, later ones mostly principal.

The formula

Canadian fixed-rate mortgages quote a nominal annual rate that compounds semi-annually, not in advance. The Interest Act (s. 6) takes interest away from a lender that does not disclose the rate on a yearly or half-yearly basis, and compounding twice a year is the market convention that follows from it. The monthly rate is therefore:

monthly rate = (1 + annual rate ÷ 2)^(1/6) − 1
payment      = loan × monthly rate ÷ (1 − (1 + monthly rate)^−months)

At a 5% quoted rate the monthly rate is about 0.4124%, a little under 5% ÷ 12 (0.4167%), so a payment worked out with monthly compounding would be slightly too high.

The default rate

The default is 4.27% a year. It is PWL Capital's expected cost of a five-year fixed-rate mortgage, a long-run expectation (75% market-based, 25% equilibrium cost of capital) and not today's posted or best rate. Anyone with a quote should enter it. The same table prices a home equity line and an unsecured line; see when the plan runs short of cash.

What the engine does

  • Computes the monthly rate and payment as above, in whole cents. Each month's interest is the opening balance times the monthly rate, rounded to the cent; the last payment is whatever clears the balance.
  • Takes the loan to be the price less the down payment, plus any default insurance premium added to it.
  • Allows an amortization of up to 30 years. Over 25 years is only available to a first-time buyer on an insured mortgage.
  • Holds the rate fixed for the whole amortization in the planner. The engine itself can take a new rate at a renewal date, and the Scenarios view uses that to show a rate change, but a plan without such a change never renews at a different rate.
  • Charges each payment as part of what a home costs each month, next to the carrying costs.

What it deliberately does not

  • Variable-rate mortgages. Those usually compound monthly, which is a lender-by-lender term, and their rate resets are not modelled.
  • Mortgage terms. The plan does not split the amortization into terms of one to ten years, each with its own renewal rate.
  • A lender's own rounding. Lender schedules round the payment and each interest figure to the cent and adjust the final payment, so a real schedule can differ from this one by a few cents a month.
  • Extra payments, accelerated schedules and prepayment privileges.
  • Qualifying for the loan at all; that is a separate test, set out in would a lender write the mortgage.

Connected to

  • Mortgage default insurance · A buyer putting down less than 20% must buy mortgage default insurance from CMHC or a competitor. The premium is 2.80%, 3.10% or 4.00% of the loan depending on the down payment, is added to the mortgage, and carries 8% Ontario sales tax paid in cash at closing.
  • What a house costs to hold · Property tax, maintenance, insurance and utilities are estimated as rates against the home's value, with sourced defaults. Property tax then grows with the home while the rest grow with inflation.
  • When the plan runs short of cash · When a month needs more money than the plan has, it draws savings in a set order, then borrows on a home equity line at 5.13% and an unsecured line at 8.38%, as far as a lender would lend. When no lender would lend more, the projection stops.
  • Would a lender write the mortgage? · Lenders test a mortgage against two ratios, GDS at 39% and TDS at 44% of gross income, using a stress-test rate of the contract rate plus 2 points or 5.25%, whichever is higher. The planner runs this screen on the income entered for today.

Sources