# What is a Compound Period?

## Definition of a Compound Period

In a mortgage loan, the compounding period is the number of times that unpaid mortgage interest is added to the principal amount of the loan.

With the exception of variable rate mortgages, all mortgages in Canada are compounded twice per year, or semi-annually, by law. If the mortgage is to be compounded semi-annually, this means that the mortgage holder can only add interest to the principal balance twice per year.

Compound interest is simply charging interest upon interest. Think of a savings account that compounds interest. If you place \$100 in a savings account paying 5% interest, compounding annually, you will have earned \$5.00 at the end of the year. In year 2, the interest earned is based on the balance of \$105.00, not the original \$100.00 deposit.

Mortgages work similarly, charging interest upon interest incurred, but as noted above, there are limits on what may be charged, or more accurately, the number of periods in which interest may be compounded. Interest charged in month 6 is added to the balance and is compounded, as is the interest charged at the end of month 12.

#### Example 1

Mr. McGillicuddy has a \$200,000 mortgage at a 5% interest rate. Funds were provided on the first of the first month of the mortgage, but the first payment was not due until the first of the following month. There will always be a month period in which the mortgage payments are behind a month from the date of the original release of funds. At the end of months 6 and 12, unpaid interest (one month worth of interest) will be added to the principal balance and charged interest.

The nominal interest rate is the actual interest rate agreed upon when arranging the mortgage. The real interest rate, or effective yield, is the actual interest rate when the compounding period is taken into account, and compound interest is applied. The real or effective yield is most commonly referred to as the annual percentage rate or APR.

The more frequent the compounding period, the higher the real interest rate will be. Since most mortgages in Canada only have 2 compounding periods per year, the real interest rate is only slightly higher than the effective yield.

#### Example 2

Mr. McGillicuddy has a \$200,000 mortgage at a 5% interest rate with a semi annual compounding date. If the mortgage mortgage payments are paid as agreed, accrued interest will be applied to the unpaid balance twice per year. The interest added to the principal balance will increase the real interest rate of 5% to an effective interest rate or APR of 5.063%.

You can use the Mortgage Comparison Calculator to calculate your APR, based upon a given mortgage rate and a built in semi annually compounding period.