I can pay whatever it seems. The calculator thing doesnt work. I have a mac. It just shows a blank screen. Not happy about that. It really looked useful to.

If it's blank, you probably don't have the latest version of Java installed. Use the Software Update from your apple menu to check that you have the most up-to-date version of Java.

I don't know of any TFSA that pays more than 2%.

A TFSA doesn't have to be a high-interest savings account. It could be a GIC, which could make 3 - 4%, or even a self directed TFSA which can hold mutual funds, stocks, bonds, or pretty much any investment. You have to think of the TFSA account as a variation of an RRSP account: it's just a special investment vehicle that has tax advantages.

By law, mortgage interest in Canada is calculated semi-annually (i.e., twice per year).

If you like math,

here is a decent web page which shows how to compound mortgage interest for both semi-annual and monthly (and more frequent) payments.

Please correct me if I'm wrong, but I thought most financial institutions calculate mortgage interest on a daily basis, though the rate they show you has to be based on semi-annual compounding. The link you provided shows how the semi-annual compounding basis can be converted to an equivalent monthly compounding basis. But last time I moved my mortgage to another bank, the transfer occurred in mid-month and they had to make adjustments to compensate for about a week's worth of interest. The adjustment amount was calculated using a daily compounding rate (obtained using math similar to finding the monthly rate). Therefore, when you make a lump-sum payment in mid month - provided the lender allows this - the mortgage principal is immediately reduced and will lower the ratio of interest/principal on your next monthly payment. It DOES make a difference if you pre-pay at the beginning of a pay-period vs the end of the payment period... you're always better off paying as soon as possible. I think I once calculated that for every day that I delayed in making a $10,000 pre-payment, it would cost me a dollar in interest.

So, getting to the OP's original question of monthly pre-payments vs one lump sum, I would vote for a third option: pay as frequently as you can, provided the lender allows you to. If you're setting aside a portion of your paycheque to go toward the mortgage, then make the pre-payments right after each paycheque is deposited (which I suppose is monthly for some people).