How We Calculate Every Number — Formulas, Sources and Assumptions

Principal and interest

Both markets use the standard amortization formula, where P is the amount financed, n is the number of payments and r is the rate for one payment period:

M = P × [ r(1 + r)ⁿ ] / [ (1 + r)ⁿ − 1 ]

The one difference that matters: compounding

In the United States, mortgage rates are nominal annual rates compounded at the payment frequency, so a monthly rate is simply annual ÷ 12.

In Canada, the Interest Act requires fixed-rate mortgages to be compounded semi-annually, not in advance. The equivalent monthly rate is (1 + annual ÷ 2)^2÷12 − 1. On a $500,000 mortgage at 5% over 25 years, that is $2,908.02 a month; the US formula returns $2,922.95 — about $15 a month too high, roughly $4,500 over the amortization. We use the Canadian formula on Canadian scenarios, which is why our principal and interest lines up with the official CMHC calculator.

Total monthly payment

The headline figure is everything due in one payment period: principal and interest, plus property tax, home insurance, any HOA or condo fee, plus US mortgage insurance. Annual figures are divided by the number of payments a year, so switching to bi-weekly rescales every component consistently.

Mortgage insurance

United States — PMI

Required above 80% loan-to-value. We estimate the annual premium from your credit band and LTV (roughly 0.19% to 1.85% of the original loan a year), charge it monthly, and remove it from the schedule when the balance reaches 78% of the purchase price — the automatic termination point. We also show the earlier date at which you reach 80% and can request removal yourself, because the difference between those two dates is real money.

Canada — CMHC-style default insurance

Required below 20% down, and priced as a one-time premium: 4.00% of the loan at 5%–9.99% down, 3.10% at 10%–14.99%, and 2.80% at 15%–19.99%. The premium is added to the principal and amortized, so it changes your payment through a larger loan rather than as a monthly line. Provincial sales tax on the premium (8% in Ontario, 9.975% in Quebec, 7% in Manitoba, 6% in Saskatchewan) is shown as cash due at closing, because it cannot be financed.

Canadian rules we enforce

Minimum down payment: 5% of the first $500,000, 10% of the portion from $500,000 to $1,500,000, and 20% at $1,500,000 or more, where insurance is unavailable.
Insured amortization: capped at 25 years, or 30 for first-time buyers and newly built homes.
Stress test: the qualifying payment uses the higher of your rate plus 2% or the 5.25% benchmark.

Accelerated payments

Accelerated bi-weekly takes exactly half the monthly payment and charges it 26 times a year, so you pay 13 monthly payments' worth annually. We do not approximate this — the schedule is built period by period at the bi-weekly rate until the balance reaches zero, which is what produces the earlier payoff date.

Where the rate data comes from

Rates are pulled from open, keyless public sources on a schedule and published with the observation date of each individual series — you can read the whole snapshot at /api/rates.json.

United States — Freddie Mac Primary Mortgage Market Survey, the weekly survey of 30- and 15-year fixed rates. A term in between is linearly interpolated between those two published points rather than snapped to the nearer one, because a 20-year loan is not priced at the 15-year rate.
Canada — Bank of Canada (Valet API). We quote the market rates a borrower can actually get: the 5-year fixed rate for a high-ratio mortgage and the estimated variable rate. We deliberately do not price mortgages at the chartered banks' posted rate (currently 6.09%), which is far above what anyone pays and would overstate every Canadian payment on this site.
Your credit band adjusts the estimate by a published typical spread, offered as a one-click suggestion rather than applied silently.

If the snapshot ever falls more than about a week and a half behind its source, the calculator says so next to the rate instead of quietly showing stale numbers.

Where the other regional data comes from

Property tax: state and provincial effective-rate averages. Actual rates are set municipally and can differ substantially within a state.
Home insurance: regional average annual premiums for roughly $300,000 of dwelling coverage, scaled with the home price on the assumption that dwelling cover is about 80% of the purchase price — land is not insured.

Every autofilled value is a starting point you can overwrite, and once you do, changing your state or price will not overwrite it again. Property tax, insurance and fees are also three independent switches: turning one off removes it from the payment and the chart, keeps the amount you typed, and says on the result what the number now leaves out.

What the AI briefing does and does not do

The optional AI briefing is given figures this engine has already calculated and formatted, and is instructed not to produce any of its own — no arithmetic, no invented rates, no numbers that are not already on your screen. Its job is prioritising and explaining, not calculating, which is why a briefing can never disagree with the calculator beside it. It is written per request, never stored, and the calculated suggestions work with or without it.

The plan PDF

The two-page PDF is composed for paper by a dedicated service — its own grid, its own charts, its own type — rather than being a print-out of the web page. Page one is the scenario, the payment breakdown, the amortization curve and where you stand at a few checkpoints; page two is the steps, the milestones, questions to ask a lender, and where to verify the figures. It is capped at two pages by design, and that cap is covered by tests.

What we do not model yet

Adjustable-rate mortgages (US) and renewal-rate scenarios (Canada).
Land transfer tax and first-time buyer rebates by province or state.
Property appreciation — equity figures reflect principal paid, not market value.
Income-based affordability limits, beyond the Canadian stress-test payment.

Common questions

Why does the Canadian mortgage payment differ from the US formula?

Canadian fixed-rate mortgages must compound semi-annually under the federal Interest Act, not monthly. The equivalent monthly rate is (1 + annual rate ÷ 2)^(1/6) − 1. On a $500,000 mortgage at 5%, this produces a payment about $15/month lower than the US formula — roughly $4,500 saved over 25 years. Section 6 of the Interest Act requires this compounding method for all Canadian mortgages with a term longer than six months.

How is PMI estimated in the calculator?

PMI is estimated from your credit band and loan-to-value ratio using published rate tables (roughly 0.19%–1.85% per year of the original loan). The monthly charge is removed from the amortization schedule at the exact month your balance reaches 78% of the original purchase price — the automatic cancellation point required by the federal Homeowners Protection Act. You can also request removal at 80%.

Where does the CMHC premium schedule come from?

The CMHC default insurance premium tiers (2.80%–4.00% of the insured loan) come directly from the official CMHC premium schedule. The premium is added to the principal and amortized, so it increases your payment by raising the loan amount rather than appearing as a monthly line item. Provincial premium tax (Ontario 8%, Quebec 9.975%, Manitoba 7%, Saskatchewan 6%) is shown separately as cash due at closing.

How does the stress test qualifying payment work?

The Canadian mortgage stress test — defined in OSFI Guideline B-20 — requires lenders to qualify borrowers at the higher of (a) the contract rate + 2%, or (b) 5.25%. The calculator shows both your actual payment and the higher stress-test qualifying payment so you can see what your lender is evaluating you on.

Why does the calculator use Freddie Mac rates instead of a lender quote?

The Freddie Mac Primary Mortgage Market Survey (PMMS) is the longest-running weekly mortgage rate survey in the US (since 1971) and is the most widely cited benchmark. It represents what lenders are offering to well-qualified borrowers nationally. Your actual rate will depend on your credit score, loan size, and lender — always get a Loan Estimate for your specific scenario.

What does "accelerated bi-weekly" actually mean?

Accelerated bi-weekly takes exactly half your monthly payment and applies it 26 times per year — equivalent to one extra full monthly payment annually. The schedule is built period by period at the bi-weekly rate, producing an earlier payoff and significant interest savings. This is different from regular bi-weekly, which simply divides 12 monthly payments into 24 half-payments (no extra principal). The CFPB explains amortization schedules and how extra payments affect them.

External references

Freddie Mac — Understanding mortgage rates — how lenders price mortgage rates, the role of MBS spreads, and why quoted rates differ from the PMMS weekly average
Bank of Canada — Interest rates — official source for the Canadian mortgage rate series this calculator uses, including posted vs effective rate distinctions
OSFI — Guideline B-20 — the federal underwriting rules that define the Canadian stress test formula (contract rate + 2% or 5.25%, whichever is higher)
CMHC — Mortgage loan insurance cost — the official CMHC premium schedule by down-payment tier used in this calculator's Canadian insurance calculations
CFPB — What is PMI? — how private mortgage insurance premiums are determined, when they apply, and the Homeowners Protection Act cancellation rules this calculator models

These are estimates for planning, not a loan offer or financial advice. Confirm every figure with a licensed lender or broker before you commit to anything.