By Brent Pritchard

My wife, Sarah, and I are both teachers. Just the other day, we were talking about how nice it is to have the flexibility to choose when we want to work in the office. (Yes, teachers do work in the summer months.) The conversation was timely. Before too long, I’d be sitting down to write the week’s post which is about time.

When you’re analyzing a real-world Time Value of Money situation, here’s how it’s going to go down:

• Either you’ll have the flexibility to choose which investment yield to use or not. (See TVM Rule #3.)

Regardless of whether you have such flexibility, you will need to determine whether you can use the stated yield or rate. It’s that simple. How do we know whether we’ll have the luxury of choice or flexibility? Enter the 312 “warm-up” routine.

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):

…it takes 3 and 1 to get to 2. First you count money, next you tell time, and then you can “read and write” the true investment yield. You’ll find an entire chapter in this user manual on the topic of reading and writing “i,” which is the ultimate goal of the 312 warm-up routine.

I’ve written about the TVM Rules before. They’re important. This probably won’t be the last time I write about them. You can remember the TVM Rules with one word: indifferent. Why would you want to remember the TVM Rules? Because they were developed around the mnemonic and audible aid indifferent that helps you determine the appropriate true investment yield. Without it don’t even bother trying to work out the math.

Let’s take a look at a few words from the rearranged TVM Rules:

3. …different payment types and signs.

1. …in different points in time.

2. …correspond the time span in between periods or payments (on the timeline) and the time span of the true investment yield.

The point of the 312 warm-up routine is to determine or calculate the “i” you’ll need to apply the Mathematics of Finance as described in TVM Rule #2. But before we can do that we must cycle through the mnemonic and audible aid indifferent in a 3-1-2 manner.

First TVM Rule #3. What is the p(ay)m(en)t? In other words, a PMT or payment (PV or FV)? In further words, an even annuity or a single payment? And then you’re on to TVM Rule #1 just like that. If you’re dealing with an annuity you don’t have the flexibility to choose how you’re going to tell time. You have to use the true investment yield that matches the timing of the frequent payments.

For the real-world situations that follow, let’s say you were given a true annual investment yield of 7.7633% with monthly compounding. (Because all interest rates are expressed in annual terms right?!)

First, let’s say you’re asked to determine the future value in one year of $100 to be received today. You have the flexibility to choose which investment yield to use because you’re dealing with a lump-sum payment. If you wanted to tell time in annual terms, then you’d have your “i.” In other words, you can use the stated (true annual investment) yield. Remember, a true investment yield considers the effects of compounding! (And for the record, even if there’s no compounding during the time span of the true investment yield in the case of a true annual investment yield with annual compounding it still considers (the effects of) compounding.)

Now on to the second real-world example that considers an even annuity which contemplates monthly deposits of $100 for one year starting one month from now. In other words, the payment is frequent and level in terms of amount and timing. So, you’re using the PMT key on your financial calculator. In this example, you don’t have the flexibility to choose which investment yield to use because you’re dealing with an annuity. You’re being told how to tell time. But you still need to determine whether you can use the stated yield or rate. In this situation, only a true monthly investment yield will work. (The answer is 0.625% if you were curious.)

I’ve written about how to manipulate yields in the book and blog. That’s the point of the 312 warm-up routine, but it’s not the main point of this post which is to show you the significance and flexibility of the mnemonic and audible aid indifferent.

What true investment yield could you use for the first real-world example that considers a single payment if you were telling time with a monthly, quarterly, or semiannual time span in between periods (not payments) on the timeline? (Answers: 0.625%, 1.8867% and 3.8091%, respectively.) How many period markers would these timelines include? (Answers: 12, 4 and 2, respectively.)

Respectfully,

Brent Pritchard, Member

Boxholm Press, LLC

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.