On Compound Interest: False advertising in the Payday Loan Industry

[hfojvt]

The math really is not that hard, so I am not sure why it is not more widely known. Yet even the Payday Loan Industry Watch and the FED do not seem to understand it (or the FED pretends to not understand it)

http://www.pliwatch.org/news_article_060913A.html

"According to the U.S. Federal Reserve, loans typically total $500 or less with fees ranging from $15 to $100. As the loans typically last for just two weeks, however, annualized interest rates could reach 1,000 percent."

Which is just wrong. Rates actually reach 10,000 percent or more. Unfarkingbelievable, but true. It's the power of compounding. One example given in the articles is a loan of $300 for two weeks which charges $60 interest. That's 20% in two weeks. The Payday Loan Places multiplies 20 by 26 and advertises that as an APR of 520%. But that's not how compounding works. A $300 loan at 520% APR would charge $1,560 interest in a year's time if no payments were made. However, look at what actually happens.
300
360
432
518.4
622.08
746.5
895.8
1074.95
1289.95
1547.93
1857.52
2229.02
2674.83
3209.8
3851.75
4622.11
5546.53
6655.83
7987.00
9584.4
11501.28
13801.53
16561.84
19874.21
23849.05
28618.86
34342.63

$300 grows to $34,342.63 in just a year's time. That's not a bad little return on an 'investment' if you can find a bunch of people with the combination of stupidity and desperation enough to pay those kind of rates. That's $300 + 34,042.63 in interest. Interest/principle * 100 = an APR of 11,347.5%.

If their profitability prevents them from being closed or restricted by regulation, then perhaps they could be sued for false advertising. I think I should get a small finder's fee for this though. Not too much. Let's just say a penny on one square of a chessboard then two pennies on the next square, four on the next one and so on, until all the squares are covered with pennies. :evilgrin:

[Selatius]

1. People need the formula for calculating Effective Annual Rate when given the APR

So...

EAR = ((1 + (5.20/26))^26)-1
EAR = 113.4754

Just move the decimal place over two spots to the right by multiplying the figure by 100

EAR = 11347.54%

The 26 comes from the compound periods in a year. In this case, it was 26.
5.20 comes from an APR of 520%. Simply move the decimal place over by two.

Now, say you have a credit card with an APR of 20.49% APR compounded monthly. Then, the formula goes like this:

EAR = ((1 + (.2049/12))^12)-1
EAR = .2252 or 22.52%

[hfojvt]

2. unlike me, you may have had more than 3 college accounting classes

I am conflating EAR with APR.

Yet, these online definitions seem to do the same thing.

http://www.investorwords.com/242/APR.html

http://www.goodmortage.com/mortgage_school/MSAPR.htm

"As a means of protecting consumers from companies who did not disclose the fees or discount points associated with a particularly low start rate on an adjustable rate loan or below market rate on a fixed rate loan, APRs give consumers a way to check the true cost of a loan."

Clearly, the way they are calculating APRs does not give "the true cost of the loan." With most financial transactions being compounded quarterly or monthly, as in the credit card example you gave, there is not a huge difference between EAR and APR. 22.5 vs 20.49 is not nearly as huge as 11,000 vs 500.

[hfojvt]

3. my finder's fee

is from George Gamow's "1 2 3 infinity ..." where legend has it the inventor of chess asks for that as his reward, only it was grains of wheat instead of pennies. Like compound interest, doubling adds up far faster than our intuition says it will. The total amount ends up being $184,467,440,737,095,516.15 or 2^64 - 1 pennies.

[karlrschneider]

4. We'll have to find a planet made of pure copper to make those pennies

:D

[hfojvt]

5. good article and author on this issue

"Advance America is the nation's leading payday lender, with 2,640 stores in 36 states, more than 5,500 employees, and $630 million this year in revenues. Dollar Financial Corporation operates 1,106 stores in 17 states, Canada, and the United Kingdom. Their 2005 revenues were $321 million. Check-into-Cash has more than 700 stores; Check N' Go has 900 locations in 29 states. Almost all of these are publicly traded NASDAQ corporations."

"While the fringe economy squeezes its customers, it is generous to its CEOs. According to Forbes, salaries in many fringe economy corporations rival those in much larger companies. In 2004 Sterling Brinkley, chairman of EZ Corp, earned $1.26 million; ACE's CEO Jay Shipowitz received $2.1 million on top of $2.38 million in stocks; Jeffrey Weiss, Dollar Financial Group's CEO, earned $1.83 million; Mark Speese, Rent-A-Center's CEO, made $820,000 with total stock options of $10 million; and Cash America's CEO Daniel Feehan was paid almost $2.2 million in 2003 plus the $9 million he had in stock options."

http://alternet.org/story/45813/

Advance America is on the NYSE, has sold 79 million shares and pays a dividend of 2.9% on $50.1 million in profits per quarter.

[Wiley50]

6. I Hate To Admit It But They've Got Me

I have to live on $623/mo SSI disability
But I have to pay the payday advance store
$330 for an $300 loan each first of the month
which means I have to borrow another $300 to get me through that month.

So they get me for $30/mo times 12

or $360/yr

I'm so ashamed

But you try to live on $623/mo
and see what happens

[hfojvt]

7. there's no shame in being robbed

They take advantage of people who are desperate or cornered. I would find some way to break the cycle, but it would be too easy for me to borrow $300 from a sibling or parents. My take-home pay is only about $662 a month, but I own my own house too. It would be cheaper to float that money on a credit card even, their interest rates are generally no worse than 25%. One trouble there is that the balance can pile up instead of staying at $300.