How the mortgage payment is calculated
A fixed-rate mortgage is repaid in equal monthly instalments. Each instalment covers that month's interest first; whatever is left reduces the principal. The standard annuity formula is:
M = P Γ r(1 + r)βΏ Γ· [(1 + r)βΏ β 1]
- M β monthly principal and interest payment
- P β loan amount (home price minus down payment)
- r β monthly interest rate
- n β total number of monthly payments
In the US and UK, r is the annual rate divided by 12. In Canada, the Interest Act requires fixed-rate mortgages to compound semi-annually, so the monthly rate is (1 + annual/2)^(1/6) β 1. This calculator applies the Canadian rule automatically when Canada is selected.
Worked example
A $300,000 loan at 6% over 30 years with monthly compounding: r = 0.005, n = 360. M = 300,000 Γ 0.005 Γ 1.005Β³βΆβ° Γ· (1.005Β³βΆβ° β 1) β $1,798.65. Over the full term you pay about $347,515 in interest β more than the original loan.
Key terms
- Amortization
- The schedule by which a loan is paid down over time. Early payments are mostly interest; later payments are mostly principal.
- Down payment / deposit
- The share of the purchase price you pay upfront. In Canada, under 20% requires CMHC mortgage default insurance; in the US, PMI usually applies below 20%.
- Property tax / council tax
- Local taxes on your home. US and Canadian property taxes are a percentage of assessed value; UK council tax is banded β enter an approximate equivalent percentage.
- Escrow
- In the US, lenders often collect tax and insurance monthly alongside your mortgage payment and pay those bills for you.