How this calculator works
The interest on a mortgage depends on the rate, the amortization and the compounding convention. Canadian mortgages typically quote a nominal rate compounded semi-annually, so paying monthly uses a rate slightly higher than one twelfth of the nominal figure; US and UK mortgages usually compound monthly. Points and upfront fees do not change the payment but they do increase the real cost, because you pay them to obtain the same payment. The effective rate including fees is the annual rate that makes the payments balance the money you actually received, which lets you compare a low-rate loan with points against a higher-rate loan without them.
Formula
i = (1 + r/c)^(c/12) - 1, where c is 2 for semi-annual or 12 for monthly compounding. n = amortization years × 12. Payment A = P × i / (1 - (1 + i)^(-n)). Total interest = n × A - P. Fees = P × points + other fees. The effective rate f solves A × (1 - (1 + f)^(-n)) / f = P - fees, reported as (1 + f)^12 - 1.
Worked example
A $500,000 mortgage at 5.5% over 25 years with semi-annual compounding has a payment of $3,051.96 and $415,587.22 of interest. One point ($5,000) and $800 of fees come to $5,800. Paid from the proceeds, they raise the effective annual rate from 5.58% to 5.70%, and the total cost including fees is $921,387.22.
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Frequently asked questions
Why does semi-annual compounding raise the payment?
Interest added twice a year grows slightly faster than the same nominal rate added once a month, so the monthly equivalent is a little above one twelfth of the annual rate. The difference is small but real over a full amortization.
Are points worth paying?
Only if you keep the mortgage long enough for the lower rate to repay them. The effective rate including fees shows what the points cost in rate terms, which is easier to compare than a dollar figure.
Is this the same as the APR on my disclosure?
It is similar in intent but not identical. Disclosure rules specify which fees count and how the rate is annualized, so a lender APR can differ slightly from the figure here.
Does the rate change over the term?
This calculation holds the rate for the whole amortization. A real mortgage renews before the amortization ends, and the rate at renewal is unknown.