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That Payday Loan

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Note: You can use any financial calculator to do this problem, but if you want the BEST, you can get our 10bii Financial Calculator for iOS, Android, Mac, and Windows!
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THE SCENARIO Recently, Representative Katie Porter of Califorina's 45th District, questioned Kathy Kraninger, the Director of the Consumer Financial Protection Bureau (CFPB), about the Annual Percentage Rate (APR) of an example loan that could be procured from FlashApply Payday Lender. The example Rep. Porter used had a 2-week term, and used simple math rather than time-value of money (TVM) math, but for short terms, the two are very nearly identical. However, if you know how to use a financial calculator, you may not be clear on how to solve a problem like the one Rep. Porter posed to Dir. Kraninger. So that's what we're going to do today, in terms that are easy to plug into the financial calculator without changing the Payments Per Year setting. The question: If I borrow $200 from a payday lender with a $20 origination fee and $20 in interest accrued over the course of a single month, what's the equivalent rate of interest on the loan? Assume that all fees and interest are due when the loan is repaid.
THE SOLUTION This one is straightforward, and you'll notice that the answer we get differs from the answer Rep. Porter came up with. We'll discuss why after finding our number. First things first, make sure the calculator is using 12 Payments per Year. N: 1 (The loan is due after a single month) I/YR: (This is what I'm trying to find) PV: 200 (I'm borrowing $200) PMT: 0 (All the fees and interest are due when the loan is repaid) FV: -240 (At the end of the month, I have to pay back the $200 I borrowed, plus the $20 origination fee and $20 in interest. $200 + $20 + $20 = $240.)

I'm paying the equivalent of a 240.0% annual interest rate on this loan.

Rep. Porter's math revealed that the rate in her example was an even more egregious 520%. How could she have gotten it so wrong? Well, the simple answer is that she didn't. And neither did we, even though our answer is significantly different than hers. How could this be? The simple answer here is 'time'. Rep. Porter's example used a 2-week payback period, and ours used a 1-month payback period. There are 26 2-week periods per year, and 12 one-month periods in a year. So when the same amount of money is due much earlier (or more often), the equivalent annual rate goes much higher. To put it another way, if we were to repeat this loan as many times as possible throughout the year, Rep. Porter's borrower would pay the $40 in interest and fees 26 times per year, and I would pay it a 'mere' 12 times. Since her borrower would pay the $40 more than twice as many times as I would, it's no surprise that their APR is more than twice what mine is.

What do you think? Did you figure out the answer to Rep. Porter's question when she asked it (Dir. Kraninger did not)? Does doing so make you more or less likely to want to take out a payday loan? Let us know in the comments!