On Interest Rates
Interest rates strike nonfinance people as so abstract that we need a metaphor (or two) for understanding them. The point of this chapter is to provide a couple of metaphors you can use to understand what interest rates are, and what interest rates do. And ideally, how interest rates can make you wealthy or keep you poor.
Parenthetical Book Structure Thoughts
Stepping back from that short-term goal for one moment, however, I want to give some further guidance as to how this entire book is structured and how you can choose to read it.
This chapter and Chapters 4 and 5 that follow are the only “technical” parts of the book. By technical I mean they involve a little bit of math. In that sense, they would be greatly enhanced by opening up a spreadsheet and then by using the text as a sort of workbook to help you with that spreadsheet. The math is accessible to junior high or early high school students and never gets beyond the application of algebra. It also uses exponents, otherwise described as “a number raised to the power of another number.”
However, to the math-allergic among you, I understand this could be as appealing to you as green olives and anchovies are to me.
So, let me preface this section with the following: Chapters 6 through 21 do not require any math to understand. You can grasp the main concepts without tickling your math-brain, and you can absolutely get wealthy applying the concepts and leaving behind your calculator and spreadsheet. If you find math terrifying, you have my permission to skip ahead to Chapters 6 through 21. Just promise me you’ll eventually come back to the beginning?
Chapters 6 through 21 are greatly enhanced by an understanding of interest rates from this chapter and the math of Chapters 4 and 5. My justification for claiming that this book will make you money is built largely on an understanding of interest rates, compound interest, and discounted cash flows, the subjects of Chapters 3, 4, and 5.
The reasons I’ve placed the math in this book upfront—knowing it will turn off some readers—are that I feel extremely passionately that:
OK, that’s it for the moment on parenthetical book-structure notes. Let’s get back to …
Interest Rates in Practice
Let’s start with the basic mechanics of interest rates, before moving on to the theoretical and metaphorical.
If I lend my $100 to my neighbor Bob for a year at a 6% annual interest rate, the stated interest rate means that I will receive $6 back from Bob at the end of the year, in addition to my original $100, because $6 is 6% of the original $100.
Conversely, if I borrow $100 from Nina and agree to pay an 8% annual interest rate on the loan, I will owe Nina both the $100 back as well as $8, for a total of $108 at the end of 1 year.
Borrowing and lending money generally involves charging a percentage of the original amount as interest, which compensates the lender by returning a larger amount of money to him or her in the future.
Why does the lender need more money in the future than he or she had lent today?
Ah, so glad you asked.
The real answer is not—as you might first suspect—because lenders are greedy and covet more money. I mean, lenders might indeed be greedy, but that’s not the reason for the practice of charging interest.
The real answer comes from the concept known as the time value of money.
The Time Value of Money Concept
OK, one more brief definitional segment before we get to the interest rate metaphors: the time value of money (TVM) concept says that money in today’s terms is always worth more than the same amount of money in tomorrow’s terms.
One way to understand this intuitively is to imagine you could be given the choice of receiving $1,000 today, or $1,000 sometime in the future, say, 5 years from now. Most people, the TVM concept posits, will want to receive $1,000 today, because it’s inherently more valuable today than in the future. The “more value” comes partly from the fact that we could do stuff with the money today, and we can’t really do stuff right now with money that’s only going to arrive in 5 years.
The “more value” also partly comes from the fact that it’s a risky world and we might never get a chance to receive the $1,000, either because we pass away or the person offering it may not be able to deliver on his or her promise.
A third reason for the TVM is that in many situations we lose the value of money through inflation—meaning we will be able to buy less with $1,000 in 5 years than we can buy today.
The commonsense cliché “a bird in the hand is worth two in the bush” approximately captures pretty well the TVM concept, highlighting that money we can have today is more valuable than some future money that we may or may not ever get to receive.
There are probably other reasons for the TVM, this idea that money today is more valuable than money in the future, but you don’t necessarily need an economist’s view for the TVM to work for you.
The main reason to know this for getting wealthy is that we need a way to link—mathematically—the value of money today with money in the future.
That is really what interest rates help us do.
OK, back to my interest rate metaphors.
The Bridge: Metaphor Number One
Functionally speaking, interest rates are a bridge.
The interest rate is the mathematical bridge that links money today to money in the future.
If we have money today, we can figure out precisely how much money we can turn that into at some future date, according to our interest rate. When our $100 today becomes $106 one year into the future, we need the 6% interest rate bridge to get there.
One main reason I want to use metaphors for talking about interest rates is that the concept of “interest rate” actually goes by many names, depending on the context. Yield, discount rate, return, and internal rate of return (IRR) are all related concepts that act as bridges between money today and money in the future.
All of these—interest rate, yield, discount rate, and IRR—do the same thing. All of these concepts refer to the number, usually expressed in annual percentage terms, that connects today’s money to future money.
If we want to figure out how our $100 becomes a larger amount of money 14 months or 8 years or 38 years in the future, we will need to move from interest rate to these other concepts—yield, discount rate, and IRR—that all serve the same function. Mathematically, they all mean the same thing. They are the bridge between money today and money in the future.
The main points of Chapters 4 and 5—just to preview a bit more—are to explain how this mathematical bridge works in practice.
In Chapter 5 in particular, we can see how a known amount of money 38 years from now, for example, can link back, through our metaphorical interest rate bridge, to a precise amount of money today.
If I want to have $1,000,000 38 years from now, I think it’s useful to know how to link that back to a specific amount of dollars today. With a 6% interest rate, or more precisely the equivalent concept of a 6% yield or 6% discount rate, I can immediately figure out, using a simple spreadsheet formula, that today’s dollars have to be, specifically, $109,238.85.
Another way of stating that is to say I could start with just $109,238 today, earn a 6% annual compound return, and I will finish in 38 years from now, with $1,000,000. My reason for this chapter and Chapters 4 and 5 is that a 27-year-old, who has not yet planned on retirement at age 65 (but ought to!), might find this useful information to know.
The interest rate bridge—using the formulas we explore in Chapters 4 and 5—explains precisely how to calculate the change from money today into money in the future, as well as the reverse, how money in the future is equivalent to money today.
In mathematical terms, the bridge metaphor helps us connect two places: the present and the future, as it relates to money. With the bridge metaphor, we conceive of money turning into something else, money changing into something larger, as it crosses the bridge. Money travels from this side of the bridge to the other side. Money moves.
With the next metaphor, however, we conceive of ourselves as moving.
The Monorail: Metaphor Number Two
We are all, wittingly or not, willingly or not, dealing with money as we move through our lives. For many—OK, for the vast majority of us—money may seem like an impediment, a force that slows down our progress. If it wasn’t for the need to reckon with money, we might think in our more frustrated moments, then we could really get ahead in life.
That frustrating feeling of pushing against a difficult force is the backward monorail many of us are on, as we pay interest on our debts.
You see, interest on money acts like a moving monorail, constantly either propelling you forward or pushing you back.
When you pay interest on your loans, for example, you’re on that monorail. To pay back the $100 you borrowed, you’ll need to come up with $106 at the end of the year, to use our earlier simple example of a 6% annual interest rate loan on $100. That extra money you have to produce is the force against you. It’s the backward monorail that seems to keep you from getting ahead.
As we’ll discuss in later chapters, the monorail is typically much tougher than that $6 on a $100 loan, for two reasons.
First, as we’ll discuss in Chapter 6, borrowing rates are rarely as low as 6%, meaning the majority of us struggle to keep up against a much faster monorail than my simple example above. The average 12% rate on a credit card, or the typical maximum legally allowable 29.99% annual rate on credit cards, makes for very fast-moving monorails indeed.
The awful truth is that nobody who makes a practice of paying on high-interest credit cards will ever be able to get ahead against that difficult, backward-moving, monorail.
Second, as we’ll talk about in Chapter 10, income taxes mean that many of us have to earn 25%–35% more than $106 just to pay back a $100 loan. What I mean is, if you pay a 30% income tax rate and you want to pay off your $100 debt, you’ll have to work to earn $151.43.1 The federal government will then collect its $43.45 (because that’s 30% of earnings), leaving you with $106, sufficient to repay your loan.
So in effect, paying back the $100 loan will cost you not $106 but rather $151.43.
Between taxes and high interest, you end up having to sprint against a moving monorail just to try to stay in one place.
That’s some depressing news.
Getting Ahead on the Monorail
But here’s an optimistic thought: the monorail also moves the other way. Interest rates on your money—also broadly understood as yield and return—can move you forward. When interest rates work in your favor—specifically, when you are a lender or an investor—your money today grows into larger amounts in the future without you hardly even trying.
If you have accumulated savings available for investment—and we’ll talk in Chapter 13 about the specific conditions for that—then you can hop on the forward-moving money monorail. Without much effort you will get ahead—you will be propelled ahead by the growth of your own money.
For wealthy people, money they have today for investment simply grows into larger amounts of money tomorrow. For wealthy people, they can choose a slow-moving and safe monorail, historically earning 1% to 3% annual return, or they can choose a more volatile but ultimately faster monorail, earning above 5% per year. Done correctly, this wealth building requires little skill or effort.
I use the monorail metaphor to present this phenomenon because wealthy people with the right approach to investing cannot prevent themselves from having more money in the future. Just by standing still. Just by doing absolutely nothing. Money just grows on money, pretty much all by itself, if we can get ourselves out of the way and let it. If that sounds like something you might be interested in, read on.2
Preparing for Math: A Preview
The math formula of the next two chapters depends on four things, each of which I’ve introduced in metaphorical terms in this chapter. Math, the language of symbolic variables, is just a further abstraction of my metaphors.
Using the bridge metaphor, the four variables are:
In the next chapter I introduce shorthand letters for these variables, in order:
Just to complete the preview, and to acclimate you to the most powerful mathematical force in the known universe, I want to write out the math formula that shows how money grows inevitably, powerfully into the future. I feel very strongly that spending a little bit of time with this formula—ideally engaging with it in a spreadsheet—can help incentivize you to get off the backward-moving monorail of debt and get you on the forward-moving monorail of wealth.
The compound interest formula we’ll explore in Chapter 4:
FV = PV ∗ (1 + Y)^N
That’s it?
Yup, that’s it.
We’ll address this in (excruciating) detail in the next chapter.
In the meantime, I hope to inspire you to examine whether the monorail you are currently on—the interest rates that affect you and your money—moves you forward or whether it moves you backward. I hope you embrace the optimistic thought that even if right now you find yourself working twice as hard just to stay in one place on a backward-moving monorail, you can flip that switch. In the future, you could let yourself be propelled forward by the same monorail.
It’s not easy to do, but it’s also not complicated to understand.
1If you’re looking for the quick math I did to come up with $151.43 pretax earnings (PTE), the formula I used is just the amount of net after-tax money (NATM) divided by 1 minus the tax rate (TR) Algebraically you could write this as PTE = NATM/(1–TR). So, $106/(1–30%) gets me to $151.43.
2My favorite faux-philosopher Jack Handey has a great line that sums up how the monorail does, and does not, work for you, depending on whether you are wealthy already or not. “It’s easy to sit there and say you’d like to have more money. And I guess that’s what I like about it. It’s easy. Just sitting there, rocking back and forth, wanting that money.”