Claims of high interest from payday lenders involve bad math

Watch Calculator

You can do the math on a watch calculator, and it still doesn't add up. Image from Wikimedia Commons.

One of the claims you hear about payday lenders is that the APR charged for payday loans is more than 100 percent per year. Granted, there is a kernel of truth to it, but only if you happen to take one particular view. The supposed high interest is among the reasons that the financial reform bill calls for further restriction on payday lending. When thought about critically, it seems to be like hunting coyotes when Grizzly bears are the problem.

First, what is APR?

APR stands for Annual Percentage Rate. APR can be calculated in different ways, and standards differ between institutions and by regulations of any given country, but that is a different topic. The way the figures for the fees for payday lenders are calculated, according to

APR = [(interest rates or fees/amount being loaned) X (days of one year/the term of the contract)] X 100.

So, let us assume a person borrows $200 and is charged $15 in fees for a loan that is due in 14 days.

$15/$200 = 0.075

365 days/14 days = 26.0714

Now, we multiply those two figures:

0.075 X 26.0714 = 1.955

Multiply that by 100:

1.955 X 100 = 195.5 APR.

Now, the going assumption is that this APR rate would compound again and again were the loan to extend over the entire year, which it certainly does not. The loan is only for 14 days, not 365.

A truer picture of APR

If one were to take the view that the fee of $15 were to apply to every two weeks of the year, it would look like this:

$15 per every two weeks, and 52 weeks per calendar year.  There are 26 two week periods per year, so:

$15 X 26 yearly two week periods = $390 total interest

Now if we were to divide the total interest by the principal:

$390/$200 =  195 percent.

Though 195 percent is right around the figures above, a person who borrows a cash advance or payday loan of $200 with a $15 fee certainly does not repay $390, they repay $215.

So looking the sum total:

$200 + $15 = $215

The difference in total paid, less the principal:

$215 – $200 = $15.

If we divide that over the principal:

$15/$200 = .075, or 7.5 percent. That doesn’t seem usurious to me.

Easier targets

Now, unlike payday loans, credit card interest always compounds monthly. Also, unlike payday loans, you don’t close a credit card two weeks after you open it.  Thinking in those terms, are we sure that government should be regulating payday lenders with the financial reform bill before other forms of consumer credit?

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