A FEW YEARS AGO A MAJOR TRUST company advertised during RRSP season with a slogan that went something like this: "You do the living, we’ll do the math". Although this jingle is catchy, it implies that the mathematics of life is just too complicated for the average person on the street to comprehend. This is completely untrue and when it comes to understanding mortgages this article will clear up some misconceptions on the subject.

Let us consider two hypothetical mortgages. The Jones family and the Smith family live side-by-side in suburban Vancouver. On January 1, 2000 each takes out a mortgage on their home of $100,000 bearing interest at the rate of 12% per annum. This means that, as a minimum, they will each pay $12,000 of interest per year and any payments in excess of that figure will be used to reduce the outstanding principal. However, there is one difference between the neighbors. The Jones mortgage (Mortgage A) is calculated on an annual basis, so the $12,000 interest cost is calculated as $100,000 x .12.

The Smith mortgage (Mortgage B) is calculated on a semi-annual basis so that the interest cost for the first six months is determined by $100,000 x .06 (.12 divided in half) for the first half of the year, and calculated in like fashion for the second half of the year. When the two $6,000 interest calculations are added together, they result in $12,000.

As you can see, if neither family pays any money toward principal, by December 31, 2000 each has paid an identical amount of interest. The difference comes in when you calculate how much principal is owing by the families on that date.

Although the Jones and the Smiths borrowed the same amount of money and paid the same amount of interest, the "effective interest rate" between the two mortgages was different. Without going into the specifics of the calculations, Mortgage A has an effective rate of 12% while Mortgage B had an effective rate of 12.36%. This is because of the timing of when the interest payments must be made. The first interest payment for the Jones is on December 31, while the first interest payment for the Smiths is six months earlier, on June 30. Although the payment is one half the amount, the fact that it is due sooner causes the effective interest rate to become higher. So, the more often the interest is calculated, the costlier the mortgage becomes.

Whether this is a good or a bad thing depends upon which side of the table you happen to occupy. If you are the investor, you want the funds that you have lent out to attract interest on a semi-annual basis. However, if you are the borrower, you would prefer annual compounding.

Of course, most mortgagors do not want to be repaid in semi-annual or annual instalments. They want payments more frequently, usually monthly. So they take the effective interest rate as calculated above, and translate it into monthly portions that maintain the contracted cost of borrowing.

Besides the interest rate and its frequency of calculation there are several additional factors that go into the mortgage document. These are (a) an open or closed mortgage: an open mortgage allows the consumer the right to pay off the debt at any time within the contracted period provided that he pay a penalty to the lender at the time that it is exercised. In most cases the penalty is an increase to the interest rate of the mortgage of one-half of one percent. A closed mortgage, on the other hand, is a binding agreement that the debt will not be extinguished before the term of the contract has expired; (b) term and amortization period: the term of a mortgage is the amount of time over which the contract will extend. It is the time from the date that the funds are advanced to the borrower until the last payment is made and the contract completed. Today, most mortgages run for a period of between six months and five years, and, as a rule of thumb, the shorter the term, the lower the interest rate. The amortization period is the amount of time over which the debt will be paid off if the contract is renewed at the same rate of interest. Historically, the period of amortization for residential mortgages has generally been between twenty and thirty years. Today, however, with many families having two incomes, it is not uncommon to see much shorter amortization periods. A longer amortization period results in a lower monthly payment but a higher total interest cost over the term of the contract (please see the accompanying table); (c) variable rate mortgage: up to now we have assumed that the interest rate of the mortgage had to be maintained throughout the term of the mortgage. This is not the case. Since most mortgage payments are made up of an interest component and a principal repayment component, when the interest rate fluctuates, the balance between them shifts. With a variable rate mortgage, the interest varies with the current market rate. Typically, the monthly payments remain constant for the term of the mortgage but the amount of each payment that is applied to the principal repayment will either increase or decrease according to a drop or rise in interest rates; and (d) optional clauses: when negotiating a home mortgage, it is possible to include a clause that will allow the mortgagee to significantly pay down the mortgage prior to the end of its term. One such clause, for example, may provide for a payment, without penalty, of say ten percent of the debt’s outstanding balance on each anniversary of the mortgage. Other important clauses will allow the borrower to renegotiate the terms of the mortgage, almost always with the payment of a penalty, should interest rates drop considerably during the term of the mortgage as well as the right to transfer the mortgage to a third party should the property be sold.