Mortgage Payment Calculator

Formula

PMT = P × [i(1+i)^n] / [(1+i)^n - 1]

Enter Values

Loan Amount ($) *

Total mortgage or loan amount borrowed. In Canada, this is typically the home price minus down payment (minimum 5-20% required). In the US, conventional loans require 20% down to avoid PMI.

Annual Interest Rate (%) *

Annual interest rate as advertised by the lender. Canadian mortgages compound semi-annually by law; US mortgages compound monthly. Enter the nominal rate (APR).

Loan Term (years) *

Amortization period in years. Common: 15, 20, 25, 30 years. Canadian max is typically 25-30 years; US conventional mortgages are often 15 or 30 years. Shorter term = higher payment but less total interest.

Results

Interpretation

For a $300,000 mortgage at 6.5% annual interest over 25 years: Monthly Payment = $2,021.08 | Total Paid = $606,324.00 | Total Interest = $306,324.00 | Principal = 49.5% of total | Interest = 50.5% of total. This calculation uses the standard amortization formula where equal payments cover both principal and interest.

How It Works

The amortization method calculates equal periodic payments where each payment covers interest on the outstanding balance plus principal reduction. Formula: PMT = P × [i(1+i)^n] / [(1+i)^n - 1] where i is the periodic rate and n is total number of payments. This is the standard mortgage payment calculation.

Key Points

Use for mortgage pre-approval and affordability calculations.
Canadian mortgages: interest compounds semi-annually, payments monthly.
US mortgages: interest compounds monthly to match payment frequency.
Does not include property taxes, insurance (PMI), or HOA fees.
Fixed-rate calculation - adjustable rates require different approach.

References

Broverman, S.A. (2015). Mathematics of Investment and Credit (6th Edition). ACTEX Publications. Chapter 3: Loan Repayment, Section 3.1: The Amortization Method, pages 79-85. Section 3.2.1: Mortgage Loans in Canada (pages 94-97). Section 3.2.2: US Mortgages (pages 97-99). Formula 3.1 (page 80): R = La_n^(-1) where R is payment, L is loan amount.