An Illinois PayDay lender revealed sets the dates on their loans so they’re not governed under state payday law, a Credit Slips blog student discovered after interviewing the company.

This particular lender offers two types of loans. One is for 14 days and charges $15.50 for every $100. The other is a 140 day loan that works like the 14 day loan, except every 2 weeks you come in and pay $15.50.

Illinois defines payday loans as being less than 140 days. This loan is structured specifically to fall outside payday lending laws.

Math problem: Assuming a $1000 loan, what’s the interest rate and total amount owed if you did the 140 day loan for 365 days and only paid the $15.50 every 14 days? — BEN POPKEN

Talking to a Payday Lender [Credit Slips]

tree fiddy?

ahaahahaha

ROFL – i mean.

kiloman, you my hero.

At the end of the year you would have paid $3875 in interest and you still owe the $1000.

This, shockingly and unbelievably, translates into an annual interest rate of more than 3500%. Seriously, that is not a typo, there is four digits in the annual percentage rate.

I did the math by taking 1.155 to the 25th power but you’ll want to do it in a spreadsheet or you won’t believe it.

Start with $1000 loan.

Every two weeks you have 15.5% interest.

This is the same as multiplying by 1.155

There are 26 two week periods in a year.

Put $1000 in the first box.

Then have the next 25 boxes multiply the previous box by 1.155.

The last box has $36690.19.

Take your $1000 back and the remaining 35690 is interest.

Umm wouldn’t it be closer to 350%? 3500% on a $1000 loan would be $35,000, not $3,500 by my math.

Assume that we take a $1000 loan that charges $15.50 at the end of every 14-day period and, further, assume for simplicity that we pay the principal at the end of 364 days.

364 days contains twenty-six 14-day periods. At the end of each of these 14-day periods we make an interest payment of $155. That’s a total of $155 * 26 = $4030 paid in interest.

The 14-day effective rate of interest is 155/1000 = 15.5%. To transform this to the equivalent 364-day effective rate of interest i, it’s necessary that 1 + i = (1 + 15.5%)^26 giving that 1 + i = 42.37 so that i is 4137%. The APY for the loan company is 4137% and it achieves this with a 14-day nominal rate of 403%.

It’s $15.50, not 15.50%. You’re paying a $15.50 flat fee every 14 days which means at the end of the year you will have paid $403 in interest for a simple interest rate of 40.3% and a total of $1,403.

It’s $15.50 on every $100. That is 15.5%.

Not for the 140 day loan…it’s $15.50 every 14 days.

Never mind, you’re right…I read the original article which makes it clearer.

From the post: “The other is a 140 day loan that works like the 14 day loan, except every 2 weeks you come in and pay $15.50.”

From the linked article: “Payday Lender’s installment loan is a whole other animal. It is a 140 day loan and works the same as the payday loan with respect to the postdated check. Every 14 days and for every $100 loaned, I would have to make an interest payment of $15.50. […] If at the end of the 140 days I was short on my principal payment, I could default, or rollover the loan for another 140 days at no additional cost.”

If it were a flat rate of $15.50, regardless of the loan size, some wealthy individuals in Chicago could take out very cheap loans taking a sufficiently large principal.

The $15.50 is per $100, so it is 15.5% every fourteen days.

So divide 365 by 14 to determine how many payments will come due in a year (26.07), then multiply that by $155, which is the payment, and you get $4041.07 in interest paid every year, or about 404% APR. And that’s for non-accruing interest. I’ve read about cases where interest was allowed to accrue, which can easily bring a loan into four-figure APRs.

(So I just noticed that j.a.s.o.n. said almost zackly the same thing, but I was fussier about the days. Also, I already TYPED!)

To: petrieslastword

Seriously, the APR is more than 3500%.

100% on $1000 would be $1000.

1000% interest on $1000 would be $10,000.

3500% interest on $1000 would be $35,000.

You’re just not believing because it is unfricking believable!

To: j.a.s.o.n’s first post. It should have only been raised to the 25th power, not the 26th. Just goes to show the magic of compound interest. The 3500% interest turns into 4100% in just one more compounding of 15.5%

You realize, of course, that this is just a ploy by the payday loan industry to force favorable state level legislation by demonstrating that the current laws are ineffective against them.

Sorry to add more to this silliness:

Assuming that you pay your $155.00 every two weeks like Ben’s problem says, there is no compounding effect. This is simple interest, ColoradoShark. That means that jason and spanky are right on the money.

NO!!! The true answer is .002 cents!

Why do I feel like some of the commenters in this thread work for Verizon…

This doesn’t show the magic of compound interest. The interest is paid off every fourteen days, so there’s no compounding. The interest paid in this example is only $4030, nothing near the $41377.13 that would be paid if interest were being compounded.

The 26th power is correct. The easiest way to see this is as follows: if the loan were only for one 14-day period, the correct power to use would be 1; if the loan were only for two 14-day periods, the correct power to use would be 2; here there are twenty-six 14-day periods so we compute using the 26th power of (1 + 15.5%).

It’s amazing how easy it is to dupe people into thinking that they’re getting cheap loans. Here’s a problem that was on the Financial Mathematics portion of the Preliminary Exams for the Society of Actuaries a few years ago.

A discount electronics store advertises the following financing arrangement:

“We don’t offer you confusing interest rates. We’ll just divide your total cost by 10 and you can pay us that amount each month for a year.”

The first payment is due on the day of the sale and the remaining eleven payments are monthly intervals thereafter.

Calculate the effective annual interest the store’s customers are paying on their loan.

The answer is 51.2%!

I’m pretty math challenged, but I can’t see how you get 51.2%. It seems to me that it would be more like 20%. The trick is in the wording: “We’ll just divide your total cost by 10 and you can pay us that amount each month FOR A YEAR.” Divide by ten, but make 12 payments.

IOW, you buy something for $100. Your payments are $10 each, but you make 12 of them, for a total of $120 = 20% interest.

Let’s first figure out what our monthly interest rate i is.

Assume that the total cost is C. Each month the payments are C/10. There are twelve such payments. Whatever the monthly interest rate i is, it satisfies

C * (1 + i)^12 = (C/10) * (1 + i)^12 + (C/10) * (1 + i)^11 + (C/10) * (1 + i)^10 + … + (C/10) * (1 + i)^2 + (C/10) * (1 + i).

Why does the interest rate i satisfy this equation? First, to compare values of payments that take place at different points in time, we have to “accumulate” each payment to the same point in time; this is because of the “time value of money”: $1 today is not the same as $1 a year from today. This is because if I have that $1 today then I can deposit in savings account and earn interest on it so it will be worth more than $1 a year from today. So we take each payment and “accumulate” it to how much it would be worth at the end of the year. That is what the right-hand side is computing. The left-hand side is doing the same for the principal on the loan. The two sides must be equal for the payments to pay off the loan.

This equation can be solved for i using a financial calculator and when I do it mine I obtain i = 3.503%. That is the monthly interest rate. To obtain the annual interest rate, we compute (1 + i)^12 – 1 = .512 = 51.2%.

Now, here’s a source of confusion. The total interest paid on the loan is (C/10) * 12 – C = C * (2/10) = .20 * C = 20% * C. To clear up this confusion, we again resort to the time value of money. While the payments have equal absolute dollar value (C/10), they have different time value of money values. The first payment is worth a lot more than the last payment. To make this clearer, let’s use your example of a $100 loan. At the end of the first month a payment of $10 is made. It turns out that this payment contains $3.1527 worth of interest and $6.8473 goes to reducing the principal. But that $3.1527 isn’t worth $3.1527 at the end of the year. If we didn’t have to make that stupid interest payment, we could instead sock that money away in an interest-bearing account and at the end of the year it would be worth more than $3.1527. It’s that lost interest that accounts for the difference between the interest paid being 20% of the principal and the interest rate on the loan being 51.2%.

I hope that clears things up.

Here’s something you can do get a little more insight into what I’m talking about. Go to

http://ray.met.fsu.edu/~bret/amortize.html

which is a loan amortization calculator. Key in a $100 principal, leave the annual interest rate and balloon payment fields blank, key in 12 payments per year, 12 as the number of regular payments and 10 as the payment amount. Check “Show Amortization Schedule” and click calculate. The calculator will show you a table of the payments and a breakdown of each payment. It will also tell you the interest rate.

Now, you’ll notice that the answer it gives 35.07% is different than the answer of 51.2% that I gave before. What accounts for the difference? That calculator assumes that the first payment is made at the end of the first month whereas the statement of the problem gave the first payment as being at the beginning of the first month of the loan. That is where the difference comes from.

Your example doesn’t indicate any interest added to the principal; to the contrary, the store says they don’t charge any funky interest, rather they use a simple installment payment structure. Granted, you end up with de facto interest because you make 12 payments of 10% of the principal.

Let’s do another example.

Take a loan of $1000 for one year at a monthly interest rate of .5% so that the effective yearly interest rate is (1 + .5%)^12 – 1 = 6.1678%. Assume that we make monthly payments at the end of each month for one year at which point the loan is paid off. The payments necessary to achieve this are $86.0664 which we’ll round, as the bank does, to $86.07. Assume that interest on the loan is compounded monthly.

At the end of the first month we’ll be charged .5% interest on the principal of $1000; that works out to $5 in interest. We break our payment of $86.07 into two pieces, $86.07 = $5 + $81.07. The first part pays off the interest and the second part kills off some of the principal (this is where the word “amortization” comes from; “mort” is like death as in “mortuary”, etc.) Our balance at the end of the first month is $1000 – $81.07 = $918.93.

At the end of the second month we’ll be charged .5% interest on the principal of $918.93; that works out to $4.59 in interest. We break our payment of $86.07 into two pieces, $86.07 = $4.59 + $81.48. The first part pays off the interest and the second part kills off some of the principal. Our balance at the end of the second month is $918.93 – $81.48 = $837.45.

We can continue this each month until the end of the loan. Here’s a table showing the interest paid, the principal paid and the principal remaining at the end of each month

$5.00 $81.07 $918.93

$4.59 $81.48 $837.45

$4.19 $81.88 $755.57

$3.78 $82.29 $673.28

$3.37 $82.70 $590.58

$2.95 $83.12 $507.46

$2.54 $83.53 $423.93

$2.12 $83.95 $339.98

$1.70 $84.37 $255.61

$1.28 $84.79 $170.82

$0.85 $85.22 $085.60

$0.43 $85.64 $-00.04

The negative balance after the last payment is a result of all the rounding. Now, sum the interest paid column. We get $32.84. This is only 3.284% as a percentage of the principal, not the 6.1678% that we’re being charged. We are still being charged an effective interest rate of 6.1678% per year, but because the principal is paid off in pieces, the parts that get paid off each month don’t have the full 6.1678% interest applied to them and that is why we end up paying less than $61.78 in interest.

I hope this makes it more clear what is going on in the discount electronics store example now.

In Canada, section 347 of the Criminal Code makes it a criminal offence to charge more than 60% interest per annum.

If I am not very bad at mathematics then the amount will be more than 350%. If this is true then its really amazing on the customers frontier how they are ready to take such loans. But the major point is that the payday loan system has been designed basically for short term so the repayment amount is not as high as we saw here. But if you do not pay on time then I think you are in a sort of bother.