# Annual Percentage Rate (APR)

One thing that most provinces have in common is the requirement to post the interest rate for payday loans in a standardized form so that the consumer can compare different lenders’ products.  The most common measure is Annual Percentage Rate, or APR.  This rate is non-obvious, so I will explain in this article what it is, and how to calculate it.

Interest rates for payday loans are for the most part limited to a certain percentage of the principal.  Since the term of a loan varies, the percentage of the principal doesn’t reflect the amount of utility that the borrower gets from the loan on a per-day basis.  APR attempts to quantify this in a manner that is clear to the consumer.  It tries to do this by factoring in the duration using simple mathematics, limiting to division and multiplication, unlike a more accurate measure which uses exponents.

The formula for APR is

APR = (Interest / Principal) x (365/Term) x 100

For an example, let’s take a loan of \$300 for 14 days where the lender charges 23% interest (as they would in British Columbia or Alberta).

Interest = \$300 * 23% = \$69

APR =  (\$69 / \$300) x (365 / 14) x 100 = 599.64% APR

To see how this changes as the term changes, consider the same loan but for only 7 days:

APR =  (\$69 / \$300) x (365 / 7) x 100 = 1199.28% APR

Now consider the original loan, but with 21% interest (as you would find in Ontario).

APR =  (\$63 / \$300) x (365 / 14) x 100 = 547.50% APR

The relationship is straightforward.  If the term is halved, the APR doubles.  If the interest ate is halved, the APR halves.  This is the same formula typically used for mortgage financing, and this familiarity is likely part of it’s appeal, but it really doesn’t capture the actual rate that is used by mathematicians or financial analysts who instead rely on a measure sometimes known as true interest, which is beyond the scope of this article.  Maybe next time!

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### 2 Responses to Annual Percentage Rate (APR)

1. Paul says:

Hi,

Looking for you update to this article. The APR that you discuss is the simple interest rate, not the APR.

Paul

• Alexander Alvi says:

This is the APR as defined by the government for use in this context. You’re correct that it is also called simple interest, as opposed to annualized or compound interest.