THE GLOSSARY · RATES
Effective annual rate
Two loans both quote you 19.99%. One costs you 19.99%, the other 22.12%. It all turns on one word you never read: compounding.
By the Yoseri News desk · · 1 min read
Two loans quote you the same 19.99%. One will cost you 19.99%, the other 22.12%. What separates them is the effective annual rate: what the rate really costs you over a year, once you count the interest added to the principal along the way. The nominal rate is just the one on display.
Until you know how often the rate compounds, it tells you nothing. Look at what the same 19.99% nominal gives:
| Compounding | Effective rate |
|---|---|
| Annual | 19.99% |
| Monthly | 21.93% |
| Daily | 22.12% |
You can check it yourself, it is one formula: (1 + rate ÷ n)n − 1, where n is the number of compounding periods in the year. For daily: (1 + 0.1999 ÷ 365)365 − 1 = 22.12%.
The gap is 2.13 points. On a $3,000 balance you carry for a year, that is $64 the advertised rate did not let you see.
Two useful markers. Most credit cards compound every day. Most Canadian mortgages compound every six months, which works in your favour: an advertised mortgage rate costs you a little less than the same rate compounded monthly.
Where the figures come from
The maths in this article starts from the assumptions written above. Run them again with your own figures — you should land on the same numbers.
Yoseri News is an educational publication. Nothing in this article is investment advice, a recommendation to buy or sell, or tax advice. Yoseri is registered as neither an adviser nor a dealer with any market authority.