# How to Calculate

Mortgage Payments

Information Source:

In Canada, loan interest is compounded semi-annually, rather than monthly as it is in the US. Because of the different compounding schedule, monthly payments in Canada are slightly lower than payments in the US, given the same principal, loan term, and nominal interest rate.

For example, consider a loan of $100,000 for 20 years at an interest rate of 6.6%. When the rate is compounded monthly, you pay $751.47 per month. When the rate is compounded every six months, you pay only $746.22 per month. This is a savings of $5.25 every month, which becomes a total savings of $1,260 over the course of the loan.

Computing Canadian mortgage payments is trickier than computing US mortgage payments because you must convert the semi-annual rate to a monthly rate. The formula explained below.

Converting a Semi-Annual Rate to a Monthly Rate

If the nominal interest rate is R (expressed as a decimal rather than percent), then the monthly interest rate is

(1 + R/2)1/6 - 1.

For example, if the annual interest rate is R = 0.066 (6.6%), then the monthly rate is

(1 + 0.033)1/6 - 1 = 0.00542587 (equivalently 0.542587%).

Calculating Monthly Payments and Total Interest

If the monthly interest rate is i (as a decimal), the number of years N, and the principal P, then the monthly payment is given by the equation

Monthly Payment = Pi(1+i)12N/[(1+i)12N - 1].

For example, suppose you borrow $100,000 for 20 years at a nominal annual rate of 6.6%. Your three variables are P = 100000, N = 20, and i = 0.00542587. Your monthly payments are

$100000(0.00542587)(1.00542587)240/[(1.00542587)240 - 1]

= (542.587)(3.664488)/(2.664488)

= $746.22.

The total interest paid is the difference between the sum of all the monthly payments and the amount borrowed. For example, if you pay $746.22 a month for 20 years and the amount borrowed is $100,000, then the total interest is

$746.22(240) - $100,000 = $79,092.80.