Same rate, different payment: what your lender never says about compounding

What does the quoted rate leave out?

A rate of 5% is an annual headline. Turning it into a monthly payment takes two more decisions, and your contract makes both of them without drawing attention to either.

The first is how often interest compounds. The second is what the year gets divided by to produce one period's worth. Different countries answer differently, and the answers are old, inherited from banking practice rather than designed.

Canada quotes rates compounded twice a year. The United States quotes a nominal annual rate compounded monthly. Australia, New Zealand, the UK and South Africa accrue daily on a 365 day year and charge monthly. Commercial lending often divides by 360 while counting real days.

Four conventions. One quoted rate. Four different answers.

Why is semi-annual compounding the cheapest?

Most people assume the opposite. Semi-annual sounds heavier than monthly, in the way that a larger interval sounds like a larger charge. The arithmetic runs the other way.

Compounding less often is cheaper for the borrower, because interest spends less time earning interest on itself. At 5% quoted, semi-annual compounding gives an effective annual rate of 5.0625%. Monthly gives 5.1162%.

That half a tenth of a percentage point is the entire difference between our two borrowers. On $500,000 over 25 years, it is $2,908.02 a month under the Canadian convention and $2,922.95 under the American one. Call it $14.93.

Fifteen dollars is not a story. What happens to that fifteen dollars when rates move is.

The gap is nearly nine times bigger at 8% than at 3%

This is the part that is missing from every other explanation of compounding conventions, and it is the reason the topic is worth more than a footnote.

We ran the same $500,000 loan over 25 years at every rate from 3% to 8%, under both conventions, and took the difference in total interest.

At 3% the convention costs $1,449 across the whole loan. At 8% it costs $12,904. The gap grows almost nine times while the rate only doubles and a bit.

Compounding effects scale with the rate, so this is not surprising once you see it. It is still worth stating, because it changes what the fact is for. In a cheap-money decade the convention is trivia. At the rates much of the world has seen since 2022, it is a real number.

Do daily and monthly accrual give different payments?

Here is a claim that gets made often and is wrong: that Australian daily interest calculation makes a loan cheaper than American monthly compounding at the same rate.

Work it through. A daily rate is the annual rate divided by 365. An average month is 30.4167 days. Multiply the two and the 365 cancels, leaving the annual rate divided by twelve. That is the American monthly figure exactly, not approximately.

So the scheduled repayment is the same. What differs is what happens between the scheduled repayments, and that difference is real.

Under daily accrual, money that lands on your balance starts saving you interest that day. Under monthly compounding there is no daily balance for it to reduce, so it does nothing until the period closes. This is the mechanical reason offset accounts work in Australia and have no clean American equivalent. Tax treatment is usually given as the other reason.

The convention that genuinely costs more is actual/360. Dividing by 360 while charging for 365 real days collects about 1.4% more interest than the quoted rate suggests. On a rate sheet it looks like any other number.

Is the compounding method set by law?

It is tempting to assume these conventions are legislated. Mostly they are not, and the distinction matters if you are trying to work out what your own lender is allowed to do.

The two places the method is actually mandated

India is the clean case. The Reserve Bank of India directs that interest be charged on all advances at monthly rests, with a carve-out for agricultural lending.⁵ That is a rule about the calculation itself.

Australia is a partial case, and the detail is easy to get wrong. The National Credit Code fixes the daily percentage rate as the annual rate divided by 365. But that figure governs the statutory cap on what a lender may charge, not what a lender does charge.⁴ Those are separate things. Lenders set their own divisor by contract, which is why some Australian banks use 365 every year and others switch to 366 in a leap year.

Everywhere else, the law governs disclosure

The United States regulates the APR through Regulation Z. The UK regulates the APRC through the FCA's rules. Germany requires an effective annual rate, with the duty in the Civil Code and the calculation method in the price disclosure regulation.⁶ All of these say what a borrower must be told. None says how to compound.

Canada does not mandate semi-annual compounding

Search this and you will be told, confidently and repeatedly, that Canadian law requires mortgages to compound semi-annually. It does not.

Section 6 of the Interest Act says that where a mortgage is payable in blended instalments, no interest is chargeable, payable or recoverable unless the document states the principal and the rate of interest, calculated yearly or half-yearly, not in advance.¹

Read it again. It requires the rate to be stated on a yearly or half-yearly basis. It does not require the lender to compound that way.

The penalty explains why the convention exists. Get the disclosure wrong and you lose all the interest on the loan, not some of it. Faced with that, lenders converged on the safest available reading and expressed rates semi-annually. The compounding followed the disclosure.

Semi-annual compounding is genuinely near-universal on Canadian fixed-rate mortgages, so the practical advice does not change. What changes is whether you can point at a statute and say it is required. You cannot.

There is a further complication. In 1967 the Supreme Court of Canada held that "blended" means mixed so as to be inseparable.² Quarterly instalments with a clearly stated rate were not blended, the Court found, because a simple arithmetic calculation could separate interest from principal. On that reading, section 6 may not reach ordinary amortised mortgages at all. Lenders comply anyway, since the downside of being wrong is total. The Uniform Law Conference of Canada recommended repealing the section in 2008.³ Eighteen years later it is still there.

One practical note for Canadian readers. The semi-annual convention applies to fixed-rate mortgages. Variable-rate mortgages there are commonly compounded monthly, which puts them in the American column.

What should you do with this?

Find your convention before you compare anything across borders. Your loan contract states it, though you may have to hunt. Canadian documents say so plainly, because the Interest Act makes them.

Then treat cross-border rate comparisons carefully. A 5% Canadian mortgage and a 5% American one are not the same product, and the Canadian one is slightly cheaper on the compounding alone. The effect is small against the rate itself, which is why nobody should move countries over it.

And if you are in a daily-accrual country, the convention is the reason extra repayments and offset balances work as immediately as they do. That is worth more than the fifteen dollars.