If you took out a $1,000 loan with a 36 percent annual percentage rate, how much interest would you pay after one year?

If you said $360, you’re wrong. The correct answer is $205.52.

Thomas Miller Jr., a professor of finance at Mississippi State University, has identified an education gap in small-dollar financing. In “How Do Small-Dollar, Nonbank Loans Work,” he enrolls the reader in a 101-level course — one that policymakers, journalists and average Joe consumers all stand to benefit from.

Miller focuses on four types of loans: personal loans from finance companies; payday loans; vehicle title loans; and pawn loans. Typically, the only news coverage these products get are horror stories — borrowers becoming trapped in debilitating debt cycles. The mere mention of their names might make even Gordon Gekko uncomfortable.

Miller’s question, then, is what gives? If these products are so bad, why do borrowers keep choosing to use them?

It’s a question of great relevance to the policymakers charged with promoting the financial well-being of millions of consumers. Do people choose payday loans out of desperation and ignorance — or because they draw genuine benefit from them? “It is important,” Miller writes, “for the people who control access to these products to understand the choices of the people who use them.”

On the “why” question, Miller’s answer is twofold.

First, millions of Americans experience monthly income variation. “Salaried employees get paid even when they are sick and cannot come to work,” Miller writes. “By contrast … roofers do not work when it rains. Restaurant workers do not get paid when they take a child to the doctor.” Their incomes are variable; their expenses recurring. As such, many people find budgeting to be a challenge.

Second, more than 100 million Americans have a subprime credit score or are unscored. These borrowers generally fail to qualify for more traditional financial products and services. For other Americans, a broken air conditioning unit in the dog days of summer can be fixed with the swipe of a credit card. Individuals with damaged or nonexistent credit don’t have that option.

The fluidity of these individuals’ financial needs, coupled with their restricted access to mainstream financial services, creates a market for small-dollar loans. It’s important to note that these products respond to real needs. Any discussion of regulating, reforming or even abolishing these credit lines needs to acknowledge that fact — and understand that serious consequences, for good or bad, could result from such actions.

A short read — the entire tract is under 100 pages — Miller’s book neatly weaves borrower characteristics and interest rate math with narratives about how the products work. For example, pawn loans, he tells us, are among the oldest forms of credit. Today, they are used by 1.8 million American households each year. Using a mounted moose head as an example, Miller walks the reader through a pawn transaction that is equal parts entertaining and informative.

The book is inviting and accessible, starting with the 1980s-inspired pop-art cover. (It may be the most stylish cover ever to grace the front of a book on small-dollar lending.) Even more important, though, Miller understands that most readers have difficulty empathizing with the use of stigmatized credit products like payday loans. To overcome this challenge, he frequently frames his discussion in the context of more mainstream or institutional forms of credit.

For example, he uses ATM withdrawals to explain why APR is an unhelpful measure of short-term loan cost.

“Suppose it is Friday after work, and you want to go out with your friends,” Miller writes. “You go to the ATM near your office and withdraw $50. Suppose that this ATM is not connected to your bank and that your bank will not refund the ATM fee, which is $3. Both the fee and your withdrawal will be taken out of your account on Monday by close of business.”

Miller walks the reader through the simple math, showing that this short-term “loan,” paid for by the ATM fee, carries a 730 percent APR. Few, however, would consider this transaction to be exploitative. Likewise, Miller invites the reader to question if a $15 fee — or 391 percent APR — on a $100 payday loan is inherently harmful.

This discussion brings Miller to the point made by our opening math problem: APR is often misunderstood and confusion over this concept impedes our public discourse on lending policy.

For many consumers using small-dollar, nonbank loans, monthly payments are more relevant than APR. Using a fairly basic financial equation — doable by anyone familiar with algebra — Miller shows that the monthly payment for a $1,000, 12-month personal installment loan with a 36 percent APR is $100.46.

Now, if the APR on that loan doubled to 72 percent, one might expect the monthly payment to double, as well. Not so. Rather, the payment would rise to $119.28. Interest rate math, while not exceptionally difficult, is not necessarily intuitive.

Miller’s lone foray into public policy discussions comes at this point in the book. He suggests that interest rate caps — such as the 36 percent cap recently proposed in Congress — will restrict some consumers’ access to credit. This is especially important given a recent Federal Reserve report finding that 60.4 million U.S. adults are unlikely to access credit at choice.

Due to fixed costs, the necessary break-even APR for lenders tends to fall as loan size increases. Miller demonstrates that, under a 36 percent rate cap, all loans with principal less than $2,600 would fail to produce enough revenue to exceed the lender’s costs. Imposing a 36 percent cap would all but eliminate these loans for millions of Americans that experience income variability and have damaged credit, leaving them with few, if any, options.

Economically vulnerable consumers stand to benefit most — or suffer most — from new policies on small-dollar lending. It is therefore essential that lawmakers, regulators, journalists and voters educate themselves on these complicated products before assigning them to perdition. Tom Miller’s book is a good place to start.