By Brent Pritchard

If you own it, the finance textbook that is, and you plan to keep it on your desk as a resource like I did back when I was in practice, then consider joining me in this movement against subpar finance content.

If you’re thinking, I’m in, I love your enthusiasm! But you may want to hear me out before joining me in what is currently only my cause as far as I know. There’s a simple step you can take to potentially help people who follow in your footsteps better understand the concept of the Time Value of Money. And you can take this step with your hand! Here goes nothing.

If you come across a page in a traditional finance textbook which misleads you into believing that all interest rates are annual or includes a lowercase of the letter “N” in any building block Time Value of Money equation related to a present value or future value, think about tearing it out! That’s right. Consider defacing that book like it’s nobody’s business, and thereby taking a stand! By tearing out that piece of paper which isn’t worth the paper it’s printed on, traditional publishers might finally come to their senses and change the terminology or variables used. Take a stand with your hand. (That is, unless of course you plan to resell your book or it’s on loan.) In summary, if you own it [your textbook], consider owning it [your education].

Here’s an excerpt from my book Would Your Boomerang Return? What Birds, Hurdlers, and Boomerangs Can Teach Us About the Time Value of Money (2023):

This user manual is made possible because of the simplicity related to the TVM Rules, consistency among the improved building block Time Value of Money equations, and connectivity throughout the TVM Formula that culminates in the 3-Step Systematic Approach. You won’t find any superfluous information or terminology in this handbook. Every component or piece has a purpose right down to the letter, literally.

One example of such change is the use of “N” instead of “n” in the building block Time Value of Money equations. The variable “N” represents the number of consecutive periods, or payments for an even annuity, that are subject to the same true investment yield and the same time span in between periods or payments (on the timeline). The investment period may or may not equal the total investment period.

Think back to TVM Rule #2: it’s a Time Value of Money no-no to fail to correspond the time span in between periods or payments (on the timeline) and the time span of the true investment yield.

Thus, “N” is not to be confused with “n” that represents the time span in between periods or payments (on the timeline). It’s “n” that allows you to “tell time” (on the timeline) for a given situation and to ultimately determine the true investment yield for a certain time span. In other words, “n” is in between the period markers on the timeline. The timeline is the visual representation of the total investment period, which will consist of one or more “N’s.”

It’s beyond me why so many other people have failed to recognize this important distinction and—as far as I’m concerned— incorrectly use “n” as a variable in their building block Time Value of Money equations. This shows me they’re loosey-goosey on the whole thing and may have fallen victim to the whole “We do it this way because we’ve always done it this way” line of thought.

I’m not complaining, because it’s improvements like this—not fixes, because nothing is broken—that led me to write this book. My goal is to clear things up and ultimately create the first-of-its-kind user manual for the Mathematics of Finance and the simple “tool” that is the TVM Formula. The formula includes, among other original works, the 3-Step Systematic Approach for applying the Mathematics of Finance to analyze and evaluate real-world Time Value of Money situations.

If considered in isolation, it might not appear that the use of “N” in the building block Time Value of Money equations is a change worthy of being called an improvement; however, the value of the user manual is in the whole rather than the sum of its parts.

In traditional textbooks, the use of the notation “n” in one or more of the building block Time Value of Money equations is widespread. In all fairness, I can kind of see why other people might choose to use “n” in their building block Time Value of Money equations. This may be too forgiving, but I would like to think that these other people are thinking that using the variable “n” instead of “N” makes sense because there are going to be times when there is only one “n” in an investment period or because the summation of multiple “n’s”—the number of periods (on the timeline)—won’t always equal the total investment period. I get it, but the improved definition of “N” recognizes this.

Recall that the variable “N” represents the number of consecutive periods, or payments for an even annuity, that are subject to the same true investment yield and the same time span in between periods or payments (on the timeline). There’s not even a direct reference to an investment period let alone the total investment period. Sometimes “N” will equal the total investment period. Sometimes it won’t. Sometimes “n” will equal “N,” but those instances will be few and far between. The definition of “N” has both these potential arguments covered.

Frankly, other people’s use of “n” in their building block Time Value of Money equations is probably more a result of there not having been a definitive systematic approach in print. But that’s changed with the publication of this handbook!

Another benefit that can’t be overstated is how separating “n” from “N” gets people focused on making sure to correspond the time span in between periods or payments (on the timeline) (n) and the time span of the true investment yield (i).

Another variable that you have likely encountered for building block Time Value of Money equations and the primary TVM financial calculator inputs in many traditional textbooks is “r” or “i” for the true investment yield. At first, one might think that this is not that big of a deal. But it’s a really big deal when one of the objectives is to eliminate ambiguity and create agreement by making all the pieces fit together.

For reasons that will become clear as you flip the pages of this book, I landed on the letter “i” to represent the true investment yield for more than the fact that i is the first letter of “investment” or “investment yield.” I took the liberty of eliminating the “r” variable.

In the building block True Investment Yield equation, the simple investment yield is denoted by “s.” The “s” variable remains. But since the true investment yield is—get it, “i” and “s”—what it’s all about when it comes to the Time Value of Money, your focus will be on the “i” variable.

You may find yourself rewriting other authors’ variables related to the building block Time Value of Money equations or primary TVM financial calculator inputs to make them jibe with the TVM Formula and the original 3-Step Systematic Approach, which are presented in this book. That’s OK, but the other way around won’t fly.

If you think I’m blowing this out of proportion, I’ve seen authors define “n” in their building block Time Value of Money equations as, “the number of years” and, “m” as “the number of compounding periods within a year.” See what’s wrong with this?

It is misguided to think that periods or payments (on the timeline) will always be annual. Again, I think the main culprit for why other people choose to settle for using a variable other than “N” is that they are lacking a definitive systematic approach. But just using “N” doesn’t solve the bigger problem! There’s more to it than that, which is where simplicity, consistency, and connectivity come in, and why a formula, the TVM Formula, needed to be developed. In the 3-Step Systematic Approach presented herein, you’ll be calculating the true investment yield as your “warm up” before “working out” the math. The TVM Formula, which allows you to apply the Mathematics of Finance to analyze and evaluate real-world Time Value of Money situations using the 3-Step Systematic Approach, is a one-size-fits-all tool.

Why not turn the torn out page(s) in to your finance instructor? (And if it’s helped you, I’d be honored if you would recommend that they consider using the “Boomerang book” as required or supplemental material to help finance students finally understand the Time Value of Money like the backs of their hands. The Boomerang book was written for you: whether you’re an aspiring or current finance professional or finance educator.)

Brent Pritchard is an author and college finance lecturer with over two decades of industry experience and cofounder of Boxholm Press, LLC, a family-owned-and-operated publishing company providing educational content, products, and services. He pioneers an innovative and approachable new way of learning and teaching the Time Value of Money as well as thought leadership in other business topics. His most recent book is Would Your Boomerang Return? You can contact him on his website here.