# How is mortgage in Canada calculated?

I'm taking a finance course at a Canadian university. The teacher said this time-of-money is how the banks calculate their loans and mortgages. Out of the blue, I want to try how close the formula in school match up to the real world. Here's my scenario:

Borrow \$300,000 at 3% interest, to be paid over 25 years. By law, the interest is compounded twice per year. Payment is to be made bi-weekly (26 payments per year). How much is the bi-weekly payment?

## My calculation

I first calculate the periodic interest rate:

``````r = (1 + 0.03 / 2) ^ (2/26) - 1 = 0.001145934...
``````

Then plug everything into Excel:

``````=PMT(r, 650, 300000)
``````

The result is \$654.83.

## Bank's calculation

I then go to TD Bank's mortgage calculator and plug in the parameters. The result is \$652.90 (see pics below).

## Question

How did the bank come up with their number? What did I do wrong?

• There are slightly more than 26 bi-weekly periods in a year. 26 * 14 = 364. Commented Jan 5, 2020 at 19:14
• @Nayuki Sounds like an answer to me. Commented Jan 6, 2020 at 18:35

As Nayuki points out you have too few days per year as `14 x 26 = 364` meaning you miss 1 day per year.
1. Your rate is a little too big, should be `0.001143` by using this formula `(1 + 0.03 / 2)^(14 / (365/2)) - 1`
2. You have too few periods as you use `26 payments x 25 years = 650`, which should have been `(365/14) x 25 = 651.8 ~ 652 payments`