**Canadian Mortgage Compounding**

Canadian Interest calculations for mortgages are defined by legislation. The Act states that interest can only be compounded twice annually and that all payments must be in arrears. The common terminology used is "Semi Annually and not in advance".

# Not in advance

The "not in advance" part means that the mortgage lender cannot charge the borrower interest at the start of the month, or prior to their having use of the funds. This is the opposite from residential rent, which is usually paid at the start of the month prior to the tenants use of the dwelling for that rental period.

# Semi Annually

Semi Annual compounding means that the mortgage lender cannot compound the agreed on annual interest rate more than twice a year, ie. semi annually. The result is that if a borrower takes out a mortgage at the current market rate of 10% per annum, the mortgage lender may only charge interest that will not exceed 10% compounded semi annually.

10% per annum compounded Semi Annually results in an effective yield of 10.25%. As such, for every $100 of mortgage at a 10% stated annual interest rate the lender can ask for no more than $10.25 of interest each year, equal to 10.25%.

# Effective Yield

Compounding is a function of the frequency that interest payments are made. If a borrower is required to make two interest payments a year, one at the end of month six and the other at the end of month twelve, the compounding would be semi annual. The graph below illustrates a 10% annual interest rate being compounded semi annually. Notice that the rate of 10% is divided by 2, the number of compounding or payment periods. The resulting 5% interest is charged on the balance owing at the end of month six and then again at the end of month 12.

Because this is an interest accruing loan the interest earned on interest is explicitly apparent. The interest charged at the end of month six is added to the outstanding balance and is also charged interest at the end of month twelve. The final result is that total interest has accrued to $10.25 during the year. This is exactly 10.25% of the $100 loan amount.

Mortgage payments are rarely, if ever, structured to be paid every six months. The most common payment plan is monthly. While the maximum compounding frequency allowed is semi annually the actual compounding frequency is necessarily monthly due to the common practice of monthly payment of interest and principal.

The graph below illustrates a 10% stated annual rate compounded monthly. Notice that the 10% rate is now divided by 12, the number of compounding or payment periods. The resulting rate per month is 0.83%. This rate is charged on the outstanding balance at the end of each month. Again the interest is added to the outstanding balance and is charged interest itself in subsequent months. The balance grows as interest is compounded monthly until the total interest accrued is $10.47, which is exactly 10.47% of the $100 mortgage loan amount.

# Canadian Equivalent Interest Rates

The above graph shows that a mortgage loan with a 10% annual interest rate paid on a monthly basis would result in an effective yield of 10.47% due to monthly compounding. We have established that the maximum a lender is allowed to charge if the stated annual interest rate is 10% is an effective yield of 10.25%, consistent with semi annual compounding. As such, in order to accommodate the monthly payment of mortgages and adhere to the maximum allowable yield, the mortgage lender must calculate an equivalent interest rate. This equivalent rate must be such that when compounded monthly it will result in an effective yield of exactly 10.25%, the allowable maximum given the 10% annual rate compounded semi annually.

The equivalent rate in this case is 9.7978% This rate compounded monthly will result in a total of $10.25 of interest during the year, exactly 10.25% of the $100 mortgage loan amount.

The graph below illustrates that the equivalent rate of 9.7978% compounded monthly will result in the same yield as 10% compounded semi annually.

# Canadian Mortgages

Canadian mortgage lenders must calculate an equivalent interest rate each time they issue a new mortgage loan.This rate is the actual rate used to calculate your mortgage payments. In the past Canadian mortgage factor tables, based on the Canadian equivalent rates, were used. Today Canadian calculators do the same job. In the United States there is no statute controlling the compounding of mortgage interest and as a result there are differences between US and Canadian mortgage payment calculations. The Canadian statute has the effect of capping compounding and as a result Canadian mortgage payments are slightly lower than US. To calculate your Canadian mortgage use the Canada Mortgage Cruncher.

| Effective Yields | Effective Yields | |

Stated Annual Rate | Semi-Annual Compounding | Monthly Compounding | Equivalent Rate |

10% | 10.25% | 10.47% | 9.7978% |

8% | 8.16% | 8.3% | 7.87% |

6% | 6.09% | 6.17% | 5.93% |

It should be noted that the above examples use interest accruing loans. Mortgages are not interest accruing as the interest due each month is paid and not added to the outstanding balance. While the interest paid on interest is not explicitly apparent mortgage interest is still compounded. The compounding in non interest accruing loans is a result of: the lost opportunity to use your money (invest it) because the payments are due earlier, and conversly opportunities gained by the lender to reinvest interest payments received and earn additional interest. See Compound Interest and Mortgages for a full explanation.