Quote of the Day

There are only two hard things in Computer Science: cache invalidation and naming things.

— Phil Karlton. I worked on cache memory designs while at HP and I can attest to the difficulty of cache invalidation. Also, I have struggled with coming up with meaningful names for software objects. Neither task is simple.

## Introduction

I watched a video (Figure 2) that shows Rep. Katie Porter (Figure 1) grilling the Director of the Consumer Financial Protection Bureau (CFPB) Kathy Kraninger in regards to the calculation of a payday loan's Annual Percentage Rate (APR). This blog post will show how to compute the APR for the payday loan example Rep. Porter attempts to get Ms. Kraninger to compute. I am not sure Ms. Kraninger knows exactly what APR is. The questioning is a bit uncomfortable because Ms. Kraninger is in no mood for a math exercise and Rep. Porter is not going to give up. Ms. Kraninger clearly is uncomfortable, but her discomfort is nothing compared to the discomfort experienced by a payday loan customer.

This exercise will compute the APR for a Rep. Porter's payday loan example of $200 principal with a $20 origination fee, 10% interest, and 14-day term. A finance person should be able to estimate this metric in their sleep.

## Background

### Definition

- APR
- APR is a standardized metric that represents the annualized cost of a loan, including fees and interest, to a borrower expressed as a percentage. It is not an interest rate because it includes fees and cannot be used to compute payments. Because the APR calculation is standardized, it provides a convenient way to compare the relative costs of different loans.

### Rep. Porter Video

Figure 2 shows Rep. Porter interrogating the CFPB director.

Figure 2: Rep. Porter Grilling CFPD DIrector over APR. |

## Analysis

### APR Mathematical Definition

I will use Investopedia's formula for APR (Equation 1).

Eq. 1 |

where

*Fees*are any non-interest costs associated with the loan is considered a fee.*Interest*is the interest paid on the principal.*Principal*is the amount of money owed.*N*is the loan payback period in days.

### Calculation

Figure 3 shows my calculation for the APR of Rep. Porter's payday loan example. The APR is 521%, which is a horrendous rate.

## Conclusion

Payday loans are another example of financial services companies preying on the unknowing. A 521% APR is ridiculous. Unfortunately, I see this sort of thing all the time. I caught a broker for a major investment firm try to cheat my retired mother out of her retirement money by churning her portfolio – he had no business putting an 84-year-old's money into high-risk stocks. I have also seen insurance agents sell multiple small life insurance policies to maximize their sales commissions. Again, clearly not for the benefit of their customers. I hope the CFPB eventually gets some enforcement teeth and some qualified management.

Thank you.

Hi Mark, as before thanks for sharing your thoughts.

To play with the APR formula, I wonder what would be the APR if the loan had zero interest and was just based on the fee. In that case, we have

((20+0)/200)*(365/14) = 261% which is half of the APR with interest.

With interest or not, these rates are excessive