A short-term, high-interest loan that usually must be repaid on the borrowers next payday.

Subsection 1.2.1 Interest and Risk

Banks charge different interest rates in different situations. For example, if you already have a lot of money borrowed from other banks, a bank may charge you a higher interest rate. They do this because they are less confident that you will be able to pay the loaned money back, an idea called risk.

The risk of a loan is determined using a number of factors - the two most important are the borrower's credit score and whether the loan is secured or not.

Credit scores are determined by mathematical algorithms, and are based on many different factors. We'll look at how they're determined in Section 1.6. The general principle of credit scores is that you are more likely to repay a loan if you have repaid other loans in the past. While this may seem like a reasonable system at face-value, it can create huge problems for people who haven't had access to loans in the past.

The other main factor that affects risk is whether the loan is secured. When you secure a loan, that means that you offer up something of value to guarantee that you will pay back the loan. If you fail to pay back the loan, the lender can reposess whatever you offered up. Large purchases - like cars or homes - are generally made on secured loans. If you fail to pay back the loan, the lending agency will take back the car or home which you borrowed the money for.

Subsection 1.2.2 Types of Loans and Lenders

Subsubsection 1.2.2.1 Payday Loans

Figure1.2.5."Payday Loan Place Window Graphics" by taberandrew is licensed with CC BY 2.0.

Payday loans are a type of loan often called a "loan of last resort." Anyone can take out a payday loan - the lender does not check their credit score to determine risk. Therefore, the lender must assume that everyone taking out a payday loan is high risk - even though that may not be true. Payday loans are generally made for a short term, usually two weeks (the name comes from taking a loan until the next payday, when it can be paid back). At the end of the two weeks, the borrower must pay back the amount they borrowed plus a fee. Payday loans are usually for small amounts - up to $1000 - and charge a fee of $10-$30 for each $100 borrowed [[1.11.1.2]]. So you might borrow $200 and pay it back two weeks later, plus a $30 fee. While this may not seem like much, this is equivalent to an annual interest rate of 360% - almost 20 times what a credit card might charge! In Section 1.5 we'll see how to compute how much interest a payday loan is charging.

Figure1.2.6.A short explanation of how payday lending works from the Pew Charitable Trust.

Subsection 1.2.3 Discriminatory Lending

The Equal Credit Opportunity Act (ECOA) is a federal law in the United States which prohibits discrimination in the loaning of money and other credit transactions [1.11.1.1]. The ECOA prohibits discrimination on the basis of

• Race or color;
• Religion;
• National origin;
• Sex;
• Marital Status;
• Age;
• Source of income;
• Excercise of consumer credit rights.

So if the ECOA exists, banks are unable to discriminate against different types of people, right? Unfortunately, no. While the ECOA makes it illegal to discriminate in mortgage lending, enforcement of the law is very challenging. It is very difficult to prove, in a situation where so many different factors are involved, that race or national origin influenced the lenders decision. Many lenders use complex computer algorithms to decide whether to lend to a particular borrower. Frequently, these algorithms are trained in a process called machine learning, where the computer studies data from past loans. The computer finds patterns in the data, and uses those patterns to make decision about whether to lend and what terms to offer. Because that data is based on past lending decisions made by human beings, it can (and does) contain biased decisions made by those human beings. Research has shown that these algorithms replicate the patterns of racial and ethnic discrimination that were made in the data they are trained on.[1.11.1.5] Therefore, although overt discrimination is forbidden in lending, it still occurs.

In addition to the discrimination that occurs through implicit bias (both in humans and in algorithms), the ECOA, and other similar laws in different countries, still allow banks and other lenders to discriminate on the basis of risk. Banks can choose whether or not they want to lend someone money based on how likely that person is to pay it back.

We've talked about how banks, the government, and other entities make decisions about who they will loan money to. Those decisions are made primarily on the basis of two things: credit history and access to security. If someone has a strong credit history - they have borrowed money and paid it back on time - or if they have access to property or someone with credit history to secure their loan - then they can obtain favorable terms for a loan. If they do not have either of those things, then they are left to borrow money from lenders who demand much higher interest payments.

This brings us to the question, then, of which groups of people have access to those things. Although the ECOA banned discrimination in the loaning of money in 1974, access to credit tends to be passed down through generations. If your grandparents did not have access to credit, they may not have been able to support your parents when they needed to borrow money for education or a first home - in which case, your parents would be unable to offer the same opportunities to you.

Thus, the question of who has access to affordable credit can become a question of who has access to generational wealth. Wealth is defined as the value of a family's assets - both money saved in bank accounts and investments as well as property like homes and cars - minus their debt. Studies have shown that Black Americans (as well as other people of color) have far less wealth than white Americans. In 2016, a study found that the median wealth of Black households was less than 10% of that of similar white households [1.11.1.5]. Wealth tends to accumulate in families over time. This can be direct, like inheritance, where one generation receives wealth (money or property) directly from the previous one. It can also be indirect. For example, a college student may indirectly inherit generational wealth when their parents pay for part or all of their college, or when they win a scholarship from opportunities provided by their parents. This allows them to avoid taking on debt to pay for college, which would decrease their overall wealth. This accumulated wealth, then, gives them greater opportunities to credit in their future. The effect of generational wealth can be seen in the paradoxical relationship between wealth and debt in America. Even though they have 10 times the median wealth, white households have median debt which is more than twice as high as Black households [1.11.1.5]. The debt held by white households, though, tends to be less costly than that held by Black households. Much of this discrepancy is due to access to cheaper forms of debt like home mortgages, home equity loans, and student loans. Black households tend to hold more of their debt in more expensive forms of credit like credit card debt and installment loans.

On the surface, payday loans are available to anyone. Because wealthier and white households tend to have access to other forms of credit, payday loans tend to be used primarily by poorer households and people of color. People who do not own their own home are 57% more likely to use payday loans than homeowners. People without a 4-year college degree are 82% more likely to use payday loans than those with degrees. Race, though, was the greatest predictor of whether someone had used a payday loan - Blacks were more than twice as likely (105% more likely) to have used a payday loan as individuals of other races and ethnicities, even after controlling for other factors like income level and homeownership [1.11.1.7]. If access to credit were only determined by risk - factors like income and access to security - we could expect the percentage of white and Black borrowers to be similar.

In addition to the obstacles imposed by lending discrimination and lack of generational wealth, there are other reasons why people would turn to predatory forms of lending. One very simple reason is where they live.

A study in 2019 found that there are simply fewer banks in majority Black neighborhoods. In areas where the majority of residents were white, there was an average of 41 banks & other financial institutions per 100,000 people. In majority non-white neighborhoods, that number fell to 27 per 100,000. Furthermore, banks in majority Black neighborhoods tended to charge higher fees than those in majority white neighborhoods [1.11.1.8].

The lack of banks in majority Black neighborhoods is mirrored by a greater concentration of payday lenders. A 2016 study in California found that the neighborhoods where payday lenders were concentrated were much more likely to be majority Black or Latinx [1.11.1.9]. A 2020 survey found that Black respondents were more than twice as likely to say that they lived within one mile of a payday lender [1.11.1.10]. This lack of access to low-interest lenders, coupled with easy access to high-interest lenders, is called reverse redlining. Redlining was the (now illegal) practice of singling out minority neighborhoods for mortgage discrimination, denying loans to people buying homes in those neighborhoods. Redlining is considered a major contributor to the generational wealth gap between Black and white americans. Similarly, reverse redlining creates neighborhoods without access to low-interest credit - not because of bank policies, per se, but because of physical proximity to lending institutions.

We've learned a lot about payday lenders - how they operate, why people use them, where they are, and what they do. Now that we understand the sociological aspects of the issue, let's dive into the mathematics. Mathematics can help us understand just how unfair payday lending is, how these lenders turn a profit, and study the inequity in where payday lenders are located. We'll learn the mathematics we need to analyze these issues, and then dive into some deeper exploration of the inequity of payday lending.