Credit Card Math

Credit cards are an important part of our society [citation needed], and come with an almost unlimited variety of options and perks between them. Some cards have low interest rates, others give you fancy rewards; some cards require you to have a high income, but others are free. The choices really are nearly limitless.

One of my favorite perks offered by credit cards is the ability to get cash back as a fraction of the amount you spend using the card (most likely this is actually a clever ploy to get people to put lots of money on their cards in order to run up large amounts of interest, but we'll ignore that for now). Getting straight cash can be easier to deal with than travel rewards unless you happen to use the same Miles system, and provides you with a lovely sum of money to play with usually once a year.

But not all cards are created equal. If you take a quick look at the terms and conditions of some of the major cash-back cards that are offered, you might get a graph that looks something like this (please note: Scotiabank's cards offered different rates for different purchases, such as groceries, gas, etc. As a result, they weren't included as it made direct unambiguous comparisons impossible.):

Whoa. My mistake. I set the axes equal to each other, and it almost made it look like the cash you'd get back was very nearly insignificant in the scheme of things. Silly me, that can't possibly be true...

Ok, whew, that's much better. A few things to note right off the bat:

• The graph includes annual fees, which explains why some cards start off negative
• The analysis assumes that the only important differences between cards are the cash back rewards and annual fees, and ignores differences in interest rates, maximum credit limits, minimum income requirements, etc.
• At some point in the future, CIBC's thesaurus is likely to run out of cool sounding words to add on to credit card names

The clear winner here is the Capital One card, which provides a free 1.0% cash back system which can be withdrawn from at any time, plus an additional 50% of the accrued cash back once a year (for an equivalent 1.5% cash back system). If we ignore it, though, there is actually a very neat transition between the different cards based on how much you are likely to spend each year:

If you spend:

$0-7,500: Get the TD Cash Back MasterCard. No annual fee and 0.75% cash back is a pretty decent deal, all in all. Take it and run! This is way better than its cousin, the TD Gold Elite Visa, which offers 1% but has a $79 annual fee. This range works out to credit card bills of less $625/month, and if you feel you pay more than that on average, why not try...

$7,500-24,000: The CIBC Dividend Visa. This one also has no annual fee, but its pay structure is tiered (0.25% up to the first $1,500, 0.50% for the next $1,500, and 1% after that), so it takes a while to catch up to the TD card from before. This card is the most profitable for quite a range, though! In the interest of fairness, it is worth mentioning that the RBC Visa Cash Back card is very close and works out to only $0.25 less cash back a year over this range, as the card is a constant 1% reward but cost a $19 annual fee. Its rewards, however, are capped after $25,000 spending per year, so if you're unsure of your spending you're still better to stick with the CIBC card. And if you're going outside of that range anyway, you may as well consider...

$24,000-35,300: The BMO CashBack World MasterCard. (Note how the card names get longer at higher price ranges?) This card offers an aggressive 1.25% cash back, but was offset by a $79 annual fee. If you feel like even that isn't enough to put on a card, go for either...

$35,300-50,000: The CIBC Dividend Infinite or Dividend Unlimited World Elite Visa. (Seriously how ridiculous are these names?). These cards are both tied over this range, and both cards have identical tiered reward schemes and $79 annual fees. Unfortunately, the Dividend Infinite isn't all that infinite, and its rewards are capped after $50,000 of spending, at which point...

$50,000-94,000: The Unlimited World Elite takes over solo in all its shining glory, until...

$94,000 and beyond: The BMO CashBack catches right back up. It's able to do this because its rewards run at a higher rate than the highest tier of the Unlimited World Elite. After this, there's really no stopping it (apart from, of course, the aforementioned Capital One card, which is laughing at all these other cards from the finish line). 

Really, though, if you're making enough money to be able to put $94,000 on a single credit card every year, you probably don't particularly care about which card offers you a handful of dollars more than another one.