Mortgage · Interest rates
Nominal to effective annual rate calculator.
A Canadian mortgage rate is quoted as a nominal rate compounded semi-annually. Enter the quoted rate to see the effective annual rate, and the monthly rate that is exactly equivalent to it.
A 5.00% mortgage compounded semi-annually has an effective annual rate of 5.0625%, because (1 + 0.05/2)2 − 1 = 0.050625. Its monthly-equivalent rate is (1.025)1/6 − 1 = 0.41239% a month.
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Your effective rate
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The formula
A nominal rate r compounded m times a year earns r/m each period. After a year the balance has grown by (1 + r/m)m, so the effective annual rate is EAR = (1 + r/m)m − 1. For a semi-annual quote, m = 2.
To get the rate for one month that grows to the same EAR, take the twelfth root: i = (1 + EAR)1/12 − 1. For a semi-annual quote this is (1 + r/2)1/6 − 1. Multiplying by 12 gives the nominal rate that, compounded monthly, matches your quote.
Worked example: 5.00% compounded semi-annually
Each half-year earns 2.5%. EAR = 1.0252 − 1 = 0.050625, or 5.0625%. Monthly equivalent: 1.0251/6 − 1 = 0.41239% a month. Twelve of those is 4.9487%, so a 5.00% semi-annual mortgage costs the same as a 4.9487% mortgage compounded monthly. That is why a US-style monthly-compounded calculator overstates a Canadian payment when fed the same quoted rate.
Why Canadian mortgages compound semi-annually
Section 6 of the federal Interest Act says no interest is chargeable, payable or recoverable on a blended-payment mortgage of real property unless the mortgage states the rate "calculated yearly or half-yearly, not in advance." Fixed-rate mortgages are therefore quoted with semi-annual compounding. Some lenders compound variable-rate mortgages monthly, so confirm in your documents.
Source, read 30 September 2026: Interest Act, R.S.C. 1985, c. I-15, s. 6, laws-lois.justice.gc.ca. The conversion formulas are plain algebra with no lender data. To see the payment this rate produces, use the mortgage payment calculator.
Frequently asked questions
How do I calculate a mortgage compounded semi-annually?
Convert the quoted rate to a monthly rate with (1 + r/2)^(1/6) − 1, then use the standard payment formula with that monthly rate. The mortgage payment calculator does this for you.
Is the effective rate the same as the APR?
No. The effective annual rate only reflects compounding. A cost-of-borrowing disclosure can also include fees, so do not treat the EAR as your total cost.
Why is the effective rate higher than the quoted rate?
Interest earns interest within the year. The more often it compounds, the larger the gap between the nominal rate and the EAR.
Does semi-annual compounding cost less than monthly?
Yes, at the same quoted rate. 5.00% semi-annual has an EAR of 5.0625%, while 5.00% monthly has an EAR of about 5.1162%.
Rate conversion only — confirm with your lender
This tool converts rates mathematically. It does not model fees, rounding rules or the compounding basis in your contract, so confirm those with your lender.