By Brent Pritchard

When you eat out, do you ask for your check or a bill? As far as I can tell, either appears to be correct. But for me, the word check has a positive vibe. There can be a negative connotation associated with the word bill. (Our oldest daughter is a waitress. I should ask her which is more common.) As it relates to the Mathematics of Finance, the word payment can, but need not, carry a negative connotation.

Some people, maybe those who ask for a bill in a restaurant, seem to think that there is only one way—think direction—to a payment. Like a two-way street, there are two ways to think about a payment when analyzing and evaluating real-world Time Value of Money situations.

Positive and negative. The different signs matter and inform which way the different payment types are flowing. For example, money received or withdrawn carries a positive (no sign) value, which denotes money coming into your hand. A negative sign denotes money leaving your hand, which is the case when money is invested or deposited.

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):

There are two different payment types or classifications, and four different payment subclassifications. The acronym FAT, which stands for “Frequency, Amount, and Timing,” will help you tell what kind of payment you are dealing with. A payment with no frequency is called a single or lump-sum payment, which is represented by the variable PV or FV. When there’s frequency in the payment, you’re dealing with an even annuity, even perpetuity, uneven annuity, or uneven perpetuity. Amount and timing of the recurring payments tell you whether you’re dealing with an even annuity, even perpetuity, uneven annuity, or uneven perpetuity. A series of finite, even payments—even in terms of amount and timing—is considered an even annuity and represented with the variable PMT. An even perpetuity is a kind of even annuity with perpetual timing. When the number of the payments in the series is not even (equal) then you’re dealing with an uneven annuity. An uneven perpetuity has perpetual timing but payments that increase based on the growth rate (of inflation).

Negative signs only relate to certain TVM financial calculator inputs. Regardless of which way the money is flowing, you will always be working with positive (no sign) values for the variables PV, PMT, and FV in the building block Time Value of Money equations.

When did you first realize that three of the five primary TVM financial calculator keys are payment inputs, and that (positive and negative) signs matter?

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.