Frequency of interest calculations

Much confusion exists over the difference between the frequency of mortgage payments and the frequency of interest calculations.

Traditionally mortgages were paid monthly. In recent years lenders have begun to accept mortgage payments weekly, bi-weekly, and semi-monthly, to the delight and benefit of home buyers. Yet how often the mortgage is paid is only one factor; how frequently the interest is calculated is crucial too.

The more frequently interest is calculated (or compounded, the terms being interchangeable) on a mortgage, the greater the yield to the lender, and the more expensive the loan for a borrower. Borrowers, therefore, must know how the interest on their loan -be it a mortgage, car loan, or credit card -is compounded. Lenders like loans where the payment interval and the interest calculation coincide, e.g., monthly. Car loans and personal loans are structured this way. To determine the rate of interest being charged each month when interest is calculated monthly, simply divide the interest rate by 12. Eight percent per annum calculated monthly has a monthly interest factor of .666666%. Compounded 12 times a year, it has an effective annual interest rate of 8.16%. (The effective annual interest rate is the rate of interest the lender receives on the loan at the end of the year.)

Interest rates calculated monthly are the easiest to understand and calculate for blended monthly payments. But they also cost borrowers the most. Because mortgage interest in the United States is calculated monthly, mortgage amortization books and tables from the U.S. won't work for standard Canadian mortgages, which are calculated semi-annually.

What are the benefits of having interest rates calculated semi-annually compared to calculated monthly? A rate of 8% per annum calculated semi-annually means that 4% is collected every six months. That's easy to determine if the payments are made every six months. But payments are usually made more frequently (monthly, weekly, bi-weekly, or semi-monthly). So when a mortgage calculated semi-annually is paid monthly, a monthly "interest factor" is needed which, when compounded six times, produces 4% after six months. The monthly interest factor must be less than .666666%, as that's the monthly interest factor for an 8% loan where the interest is calculated monthly, not semi-annually. For 8% calculated semi-annually, the proper monthly interest factor is .655820%.

The same with an 8% mortgage calculated semi-annually but paid weekly: then a weekly mortgage interest factor is needed that, when compounded 26 times, produces 4% after six months. Here the proper weekly interest factor would be .150549%.

Trying to figure out these interest factors manually is nearly impossible. Good computerized mortgage packages can make these calculations in seconds, to 10 decimal points or more.

Here's an example of the difference between mortgages calculated monthly and calculated semi-annually, based on a $100,000 loan, amortized over 25 years:

Another way to look at this is to compare what the different rate calculations cost a borrower at the end of the year:

• 8% calculated monthly is equivalent to 8.1345% calculated semi-annually, and 8.30% annually
• 8% calculated semi-annually is equivalent to 8.16% calculated annually
• 8% calculated annually is simply 8% calculated annually

Interest rates calculated monthly are encountered most often with second mortgages, and with loans from finance companies and credit unions. But first mortgages can legally be calculated monthly too. And the semi-annual equivalent for the interest rate does not have to appear in the mortgage document.

To eliminate all this confusion, Canadians need a common yardstick against which the true cost of borrowing can be compared on an annual basis. Otherwise, using the same quoted rate, but calculated in different ways, is bewildering -it means comparing apples and oranges, not apples and apples. What's needed in Canada is the adoption of an Effective Annual Interest Rate approach for all types of loans: mortgage, car, business, and personal. It would disclose the true interest rate being paid by a borrower and earned by a lender each year, calculated annually, regardless how often the loan was paid.

What does the expression "not in advance" mean? Having interest calculated and paid at the end of the period rather than at the start is another important difference between Canadian and American mortgages, a feature which again benefits borrowers in Canada.

The easiest way to understand the concept "not in advance" is to look at a tenant. When tenant pays his rent on January 1, he is doing so "in advance" for the month to come, the month of January. So the landlord gets the use of the money for the entire month. On the other hand, a home owner, pays his mortgage payment "not in advance." The payment for the month of January is not made on January 1. Instead it's made on February 1 (not in advance) for the month just gone by. That means the borrower, and not his lender, has the use of the money for the month of January. Most Canadian mortgages are payable "not in advance"; but still, check it out.

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