All the Numbers

How a mortgage payment is worked out

From the All the Numbers wiki · Housing

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.[1] 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.[2] 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. The interest on that loan is deductible only for the share of the home that earns rent.
  • 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 All the Numbers. 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.
  • On the house page, lets you try paying more: an extra amount every month, a lump sum once a year, or a different amortization. Each extra payment comes off what you owe after that month's payment, and the payment itself stays the same, so the loan is paid off sooner. All the Numbers takes these to be within your lender's prepayment privileges, which vary from lender to lender and are usually capped each year; above them a lender can charge a penalty.[3]

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.
  • Accelerated (biweekly) schedules, a test of extra payments against your lender's limits, and extra payments in the plan itself: they are tried on the house page only.
  • Qualifying for the loan at all; that is a separate test, set out in would a lender write the mortgage.

See also

  • A home you already own · A home you own when the plan starts is entered as it stands today — what it is worth, what is left on the mortgage, the rate and payment, when the term ends — and runs from the plan's first month, with no purchase.
  • Interest on borrowed money · Interest is deductible against rent only for money used to earn income from property, judged by what the money is used for now and not by what secures the loan. A refinance keeps the use of the loan it replaces, and a repayment reduces the deductible and non-deductible parts together.
  • 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.
  • Net worth, as the plan counts it · Net worth is everything the plan holds (cash, investment and registered accounts, homes at market value) minus mortgages, credit lines, debts and tax owing. It is not reduced for selling costs or for tax on money still in an RRSP.
  • Renting out a suite · Rent from part of your home is taxable income. The costs of the whole home are deductible only for the rented share, mortgage principal and land transfer tax are not deductible, and a loss offsets other income when the rental is run to earn money. A lender may count part of the rent when you apply.
  • Renting versus buying · All the Numbers compares a plan that buys a home with the same plan that never buys, and the money the home would have taken stays in your accounts and is saved like any other leftover cash. It shows when owning pulls ahead on net worth, if it does. It is a comparison under assumptions, not a verdict.
  • Scenarios and life events · The Scenarios page lets you drop dated events onto a copy of your plan, such as a job loss, a market drop or a rate jump, and see where net worth ends up. Each event is a change to the plan run through the ordinary projection, not a separate calculator.
  • 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 inflation, maintenance and insurance with the home's value, and utilities 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.
  • Which assumption matters most · The sensitivity chart moves one assumption at a time, down and up by a fixed step, and ranks them by how much the final net worth in today's dollars changes. Inflation is often the largest bar because it moves much more than one number.
  • 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. All the Numbers runs this screen on the income entered for today.

References

  1. ↑Interest Act, R.S.C. 1985, c. I-15, s. 6 · Fixed-rate mortgage compounding: semi-annual, not in advance — market convention anchored in the Interest Act s.6 disclosure rule; monthly rate = (1+r/2)^(1/6)−1 · effective 1985-12-12
  2. ↑PWL Capital — Financial Planning Assumptions (Market Capitalization Weighted Portfolio), mid-year 2026 data update, Table 3 (Expected Cost of Borrowing) · Default mortgage rate a year: PWL's expected cost of borrowing on a five-year fixed-rate mortgage (PWL Capital, Financial Planning Assumptions, Table 3) · 4.27% · effective 2026-08-17
  3. ↑FCAC, Mortgage fees: Prepayment penalties ("Prepayment privileges vary from lender to lender"; "Most lenders limit the allowed prepayment amount per year"; paying "more than the allowed additional amount" can bring a penalty) · Extra payments tried on /house ("Pay it down faster") are taken to be within the lender's prepayment privileges, so no prepayment penalty is charged; each comes off the balance and the regular payment stays the same · effective 2026-10-12