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Technical Methodology & The Math

This page documents the formulas and policy assumptions used in the calculator. Figures are estimates for discussion with a licensed professional—not approvals or offers.

Canadian semi-annual compounding

Canadian fixed-rate mortgages typically compound interest twice per year. The quoted nominal annual rate r (as a decimal in the formulas below, e.g. 0.05 for 5%) is converted to an effective monthly rate i for payment math:

i=(1+r2)2/12−1i = \left(1 + \frac{r}{2}\right)^{2/12} - 1

This matches the standard conversion from a nominal rate compounded semi-annually to an equivalent monthly rate used in amortization schedules.

Level monthly payment (annuity)

Given principal P, monthly rate i, and n monthly payments, the standard annuity formula for a fixed payment M is:

M=P⋅i(1+i)n(1+i)n−1M = P \cdot \frac{i(1+i)^n}{(1+i)^n - 1}

When i = 0, the tool falls back to M = P / n to avoid division by zero. Maximum loan from a payment cap uses the inverse of this relationship.

A-Lender qualification (ruleset)

For the A-Lender path we apply ratio limits consistent with common federally regulated underwriting:

  • Gross Debt Service (GDS): housing costs (stress-tested mortgage payment, simplified—property tax/heat are not itemized in this tool) are tested against 39% of gross monthly income.
  • Total Debt Service (TDS): housing plus other monthly obligations are tested against 44% of gross monthly income.
  • OSFI stress test (qualifying rate): the higher of contract rate + 2 percentage points and a 5.25% floor—aligned with public B-20 guidance for uninsured and many insured scenarios.

Displayed payments on the cards use your expected contract rates (cash flow); pass/fail uses the stress-tested payment at the qualifying rate above.

B-Lender logic (illustrative)

B-Lender and alternative lenders often operate with different risk models than major banks. In this calculator, the B-Lender path is an educational illustration:

  • Qualifying rate for ratio tests is modeled at contract rate + 1% (more flexible than the A-Lender stress test—actual lender policies vary widely).
  • Higher debt-service headroom: we use a 50% TDS ceiling in the tool to represent the kind of ratio flexibility some alternative lenders offer—not a guarantee of approval.
  • Amortization resets: extending the amortization (including toward up to 30 years in the strategy slider) lowers the monthly payment used in ratios, which can improve qualification on paper—subject to lender, loan-to-value, and product rules.

Real-world B-Lender pricing, fees, and approvals are case-specific. Use these outputs to prepare questions for a licensed advisor rather than as a substitute for an application decision.

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