Why are mortgage rates compounded semi-annually?

Ever wonder what they mean when the banker quotes a mortgage rate of 4% but then tags on the words… “SEMI-ANNUAL COMPOUNDING BASIS?  What exactly does this mean?  What effect does this have on your mortgage payments or the time it will take to pay your mortgage down.

It is an interesting question and an important one to pursue the answer to. Next time you see this posted at your bank, take a moment to ask the teller to explain to you just what this means.  Most banks in Canada  have their rates quoted on a SEMI-ANNUAL basis… while most other countries quote their rates on a monthly basis.  What exactly are they up to and why would they bother to quote it this way?

Let’s look at a hypothetical example and discover how and why some rates are compounded multiple times a year. You may be surprised to learn that you are paying more for that mortgage than you thought!!  Here’s a little tip right out of the gate. Regardless of how the posted interest is calculated just ask the loans offer what the effective rate is. That is, what rate you are really paying… that should clear things up for you.

Here is an example to help clarify:

First the assumptions.
1. Principle amount borrowed is $100,000
2. Interest rate used will be 10% (annually, monthly, and semi-annually)
3. No Payments will be made (so we can isolate the effect of the interest and its compounding)
4. Loan is taken out in January 1st and repaid on December 31st  for ease of comparison
5. All numbers rounded to the nearest dollar

ANNUAL COMPOUNDING
This is the most common form of interest , but you don’t see this used too often in the mortgage world. It just so happens to be the lowest overall  EFFECTIVE rate (what you are really paying). So would it be a surprise to you to know that this is the method banks use when it comes to paying you for the money you have on deposit such as term deposits or GIC’s.

Based upon our assumptions here is how a loan for $100,000 would look using the annual compounding method.
January $100,000 Outstanding
February $100,000 Outstanding
March $100,000 Outstanding
April $100,000 Outstanding
May $100,000 Outstanding
June $100,000 Outstanding
July $100,000 Outstanding
August $100,000 Outstanding
September $100,000 Outstanding
October $100,000 Outstanding
November $100,000 Outstanding
December $100,000 Outstanding + $10,000 Annual Interest Accrued and Compounded
Total $110,000

The interest is calculated just once at the end of the year and added to the total amount outstanding.  Remember the posted rate is still 10%… and that is exactly what you paid.

MONTHLY COMPOUNDING
Now let’s take a look at the monthly compounding strategy, a very common method used to calculate consumer loans, credit cards, student loans, retail cards, car loans, lease payments, and just about every other form of credit. This one is pretty easy to wrap your head around because so many of our expenses are calculated on a monthly basis. What you are about to see is that even though the rate you are shown is still 10%,  it is actually a higher rate of interest than we just looked at when the compounding is done less frequent.

Once again, using the assumptions made above:
January $100,000 Outstanding +$833 of monthly compounded interest
February $100,833 Outstanding +$840 of monthly compounded interest
March $101,673 Outstanding +$847 of monthly compounded interest
April $102,520 Outstanding +$854 of monthly compounded interest
May $103,374 Outstanding +$861 of monthly compounded interest
June $104,235 Outstanding +$869 of monthly compounded interest
July $105,104 Outstanding +$876 of monthly compounded interest
August $105,980 Outstanding +$883 of monthly compounded interest
September $106,863 Outstanding +$890 of monthly compounded interest
October $107,753 Outstanding +$898 of monthly compounded interest
November $108,651 Outstanding +$905 of monthly compounded interest
December $109,556 Outstanding + $913 of monthly compounded interest
Total $110,469

So even though the posted rate was 10% you paid MORE because it was compounded monthly… $469 more than a real 10% that is calculated once at the end of the year.

SEMI-ANNUAL COMPOUNDING
So now let’s look at the way a mortgage is calculated. Most in Canada are semi-annually compounded. Based upon the results so far do you think it is safe to believe that you will be paying more than the annual compounding period but less than the monthly compounded period? So if monthly compounding works out to being a higher  Let’s take a look.

January $100,000 Outstanding
February $100,000 Outstanding
March $100,000 Outstanding
April $100,000 Outstanding
May $100,000 Outstanding
June $100,000 Outstanding + $5,000 semi-annual interest accrued and compounded
July $105,000 Outstanding
August $105,000 Outstanding
September $105,000 Outstanding
October $105,000 Outstanding
November $105,000 Outstanding
December $105,000 Outstanding + $5,250 Interest Accrued and Compounded
Total $110,250

Well it looks like our assumption was correct. Compounding semi-annually cost less than a loan that was compounded monthly but all of this makes it abundantly clear that to really understand how much any loan is going to cost you MUST understand the compounding period that will be used in the calculation.

In summary, the amount of interest paid under each type of compounding is as follows:
$10,000 Annual Compounding
$10,250 Semi-Annual Compounding
$10,469 Monthly Compounding

And for your information  the interest cost would be $10,516 with Daily Compounding
So, the more frequent the compounding periods, the more interest you will actually pay even though each one of these loans will be posted with a rate of 10% . So be aware and remember… ask for the EFFECTIVE rate to get clarity.

Now just for fun check out your deposit accounts at your bank. I’m guessing every one of them will have the interest calculated annually.  The rate appears higher than what you would actually earn if the compounding periods were more times per year. Now check out your credit cards.  That rate will more than likely be compounded monthly… which makes the rate seem lower than what you will actually be paying.

So here is the general rule of thumb. When the bank is paying you they will more than likely quote a rate that will be compounded annually and when you are paying the bank  for a loan they will more than likely be quoting a rate that will be compounded monthly, semi-annually or maybe even daily.

Watch out… and be aware! Posted rates are not always what they appear to be.