By Dr. Tyler Scott, WCI ColumnistAlbert Einstein’s work is beyond my comprehension. A woefully incomplete list of his contributions includes Avogadro's Number, Quantum Theory of Light, General Theory of Relativity, Special Theory of Relativity, The Photoelectric Effect, Wave-Particle Duality, Brownian motion, the relationship between mass and energy (E = MC²), and the Bose-Einstein Condensate.
I have spent hours turning over these ideas, and I often feel dumber when I stop reading than when I started. I find him and his work fascinating. Thus, I am fascinated by what he was fascinated with.
One of the things he was most riveted with and passionate about is something that this community can understand and relate to—the power of interest. His inquisitive and mathematical brain understood better than most the profound impact of compounding interest.
Two famous quotes pertaining to compound interest are commonly attributed to Einstein.
“Compound interest is the eighth wonder of the world. He who understands it, earns it . . . he who doesn’t . . . pays it.”
“Compound interest on debt was the banker’s greatest invention to capture and enslave a productive society.”
When reading statements like these from someone with such a transcendent mind, it is understandable that conversations about interest rates are so pervasive in financial circles.
My goal today is to invite some context to those conversations, to try to quantify Einstein’s observations, and to help focus our attention on when those observations matter most and when they can be reasonably ignored.
When Interest Rates Don’t Really Matter
Cash
If I had a nickel for every email from a client that read something like the following, I’d have enough for a cocktail at The Chandelier Bar.
“Hey Tyler, thanks for the reminder to get some own occupation long-term disability insurance. I’ll get to that eventually, but in the meantime, I have a pressing question. I was noticing that the Vanguard Federal Money Market is paying 5.1% right now and my high-yield savings account is only paying 4.1%. I was thinking it makes sense to move my $60,000 emergency fund over to Vanguard to take advantage of this much better interest rate. What are your thoughts?”
I understand the impulse to ask this question and to consider making this change. As we will see shortly, a 1% interest rate difference can have a significant impact on a financial plan.
This is not one of those times.
A total of $60,000 getting an extra 1% earns an extra $600 per year before considering taxes. Remember that interest paid from a financial institution is subject to ordinary income taxes. Assuming a 40% marginal tax rate, this $600 becomes $360.
My email response to clients first quantifies the value of the proposed action and then usually says something like:
“I’m not here to scoff at $360; I just don’t think ~$300-$400 this year is going to make or break any of your short- or long-term financial goals. Also, from what you told me last time about wanting to prioritize time with your kids, I imagine the hours you would spend moving money around over the years chasing interest rates would likely bring you more happiness/value if you were checking off that list of local hikes you wanted to do as a family.”
The response that follows is often, “Wow, I didn’t realize the difference was so minimal. I’ll definitely opt for the hike instead of the extra financial chore. And I promise I’m gonna get that own occ disability insurance here soon.”
To be clear, having cash earn a reasonable rate is important. If you have a large five-figure or six-figure amount of cash parked at a local bank earning 0.02% interest, moving that money to a high-yield savings account is worthwhile. At least half of the new clients I meet are functionally earning 0% on their cash.
More information here:
Restoring the Balance Between Savers and Borrowers
Mortgage Payoff vs. Cash
A similar version of this conversation comes up when considering whether to pay off a mortgage with existing cash. Here is a comment from a recent blog post WCI founder Dr. Jim Dahle wrote about the value of a paid-off home.
“I owe $170,000 on my mortgage at fixed 3.9%. I could pay it off tomorrow, but it doesn’t make sense for me, especially considering with tax deduction that 3.9% is actually about 2.8%. The Schwab money market is paying 5%.”
First, let’s clean up a couple of issues with that comment.
Cleanup No. 1: It only makes sense to consider the after-tax interest rate on the mortgage if you itemize your taxes. The Tax Cuts Jobs Act that passed in late 2017:
- Doubled the size of the standard deduction ($29,200 for Married Filing Jointly in 2024 and $30,000 in 2025), so if your itemized deductions don’t exceed $29,200 or eventually $30,000, there is no reduction in your mortgage rate.
- Removed all itemized deductions except charitable contributions, state and local taxes (SALT), and mortgage interest for mortgages of $700,000 or less. (Note, if your mortgage is more than $700,000, you are not getting a deduction on the portion above $700,000.)
- Limited the SALT deduction to $10,000.
As a result, far fewer people itemize these days, with nearly 90% of taxpayers taking the standard deduction. Admittedly, many of those 10% who itemize are likely readers of this blog because of sizeable mortgages and/or charitable mindsets.
Cleanup No. 2: We need to reduce that 5% interest rate from the Schwab Money Market for taxes so we are making an apples-to-apples comparison: the post-tax mortgage rate they are paying vs. the post-tax interest rate they are earning. For many readers here, the after-tax interest rate being earned is likely close to 3.6%.
With our cleanup complete, we can compare the difference between:
- Paying off a $170,000 mortgage with an after-tax rate of 2.8%
- Keeping $170,000 in a safe, liquid account (i.e. money market) paying an after-tax rate of 3.6%.
How much is this 0.8% delta worth? It'd be $170,000 x 0.8% = $1,360 in the first year and a little less each year after as the mortgage balance gets ever smaller.
Again, $1,360 is nice. I’m not disparaging that amount of money. It is just my observation that most people making these kinds of decisions have routinely underestimated their pet care, gasoline costs, hair and beauty, or any other expense for the year by more than $1,360. In other words, this dollar figure is not consequential to most who are in the privileged position to contemplate this “pay off or invest” decision, but the decision gets a tremendous amount of time and energy devoted to it despite its ultimate irrelevance.
Sorry, Einstein . . . no eighth wonder of the world here.
Aggressive Student Loan Paydown
Another area I see people stress too much about interest rates is when they are looking to aggressively pay off their student loans and are considering privately refinancing their federal loans.
Let’s say a newly minted lawyer, engineer, or attending physician has $250,000 of federal loans at 6.8%. Being fully indoctrinated WCI consumers, they are committed to living like a trainee and paying these loans down within 3-5 years. They come to me as a financial planning client or during a consult at Student Loan Advice asking, “Is it worth it to privately refinance my student loans?”
The answer, of course, is, “It depends.” But in general, it usually does not make sense in these cases.
Why? Because you just don’t save that much money on a refi when you are paying down your debt quickly. This is true of all debt. In the case of federal student loans, you are also giving up a lot of flexibility and a number of protections when you leave the federal arena for the private sector.
In this example, let’s assume the best offer our new professional can find to refinance their $250,000 over five years is 5.5%. That’s 1.3% lower than their federal loans. That sounds like a lot, but how much savings does that represent? It's about $1,800 per year.
Once again, I do not mean to deride $1,800. I’m just saying that for someone making $200,000, $300,000, or $400,000, it doesn’t move the needle that much over a 3-5 year period. And, in the case of federal student loans, that $1,800 is acting as a pretty inexpensive insurance policy should your financial plan change during those five years (move, change jobs, get married, get divorced, have a baby, get disabled, etc.).
More information here:
The Benefits of High Rates on Cash
Credit Card Optimization
While we are talking about percentages, please forgive me for this brief, semi-related tangent.
I’m baffled by the lengths people will go to and the complexity they are willing to add to their lives by having eleventeen credit cards to get 3% back on gas, 4% back on restaurants, and 5% back from Home Depot vs. just having a single 2% cash back credit card. That extra 1% on gas or 2% on restaurants is not the difference between winning and losing the single-player game of personal finance.
Now, if optimizing every percentage point in every area of your financial life is a hobby that brings you joy, I love that for you, and I would never ask you to give up something you enjoy. I’m just gently pointing out that if you are doing it because you think it has a material impact on when you will reach financial independence, it’s likely not helping accomplish that goal. There are far more impactful hobbies and side gigs than saving 1.5% a year on pad thai.
In short, don’t fight small. Fight the fights that matter and leave the rest behind.
When Interest Rates Do Matter
Don’t fight small; fight big! Let’s talk about when to fight back against those bankers Einstein warned are here to enslave us with their interest rates.
Mortgages
A house is the most expensive thing most of us will ever buy. If ever there was a purchase to be hyper-fixated on its impact to your financial plan, it’s this one. Justifiably, the element of housing most people think about is the purchase price of the home. This is obviously important, and WCI has offered up several posts, podcasts, and rules of thumb when it comes to the variable of purchase price. Perhaps the rule easiest to remember is: don’t borrow more than 2x your annual income for a house. This is good advice.
The purchase price is just one factor in housing costs. Property taxes, insurance, maintenance, HOA fees, etc., are also significant, but those are largely not within our control. After the purchase price, the mathematical factor most within our control is the interest rate, and its impact is enormous. Even small changes can make a very large difference given the amount of money being borrowed and the duration over which it is paid back.
Consider a 30-year, $800,000 mortgage:
- At 7%, the total interest paid after 30 years is $1.116 million.
- At 6%, the total interest paid after 30 years is $926,700. That’s a 30-year savings of ~$190,000 compared to the 7% loan.
- At 5%, the total interest paid after 30 years is $746,700. That’s a 30-year savings of ~$370,000 compared to the 7% loan and a savings of $180,000 compared to the 6% loan.
Now we are seeing where Einstein was coming from. But remember his quote wasn’t just, “He who doesn’t understand {compound interest} pays it.” It was also, “He who understands it, earns it.”
If we were to put that monthly savings to work in an investment account earning a modest 5% annualized, what would the impact be? On the 6% loan, after 30 years, the homeowner would have an additional $438,000. On the 5% loan, after 30 years, the homeowner would have an additional $855,000.
- Total difference in wealth for the 6% mortgage owner = $190,000 + $438,000 = $628,000
- Total difference in wealth for the 5% mortgage owner = $370,000 + $855,000 = $1.225 million
E = M[ucho]C[ash]2. Preach Albert!
You might be saying, “Fun numbers experiment, Tyler, but I don’t get to choose the interest rate on my mortgage. What do you mean this is within my control?” It's true you don’t get to pick your interest rate like a shirt at Target, but you have far more ability to shop for deals than you may realize.
First, you don’t have to buy a house when interest rates are “high.” Renting is a completely reasonable housing plan and often the right one for many. Most of the urgency to buy a home is self-imposed, and being willing to ride out periods of higher rates may prove prudent. So can waiting for your credit score to improve or to establish a couple of years of income in a new job which can result in lower rates.
When you decide to buy a home, every coupon-cutting, deal-hunting, flea-market negotiating bone in your body should be primed and ready to drive down your interest rate. Far too often, people get their mortgage by asking their realtor who they recommend, calling that person, and accepting the first rate that is offered by one single mortgage broker or, worse, one single bank.
I’m astonished at the number of people in our country who are willing to sleep overnight in a snowy Best Buy parking lot to save $500 on a TV but who won’t take a couple of hours to shop far and wide to save $100,000 on their mortgage.
At 40 years old, I have purchased three homes (all primary homes; I find real estate investing radically overhyped and mathematically inconsequential for most, but that is a WCI fight for another day). In each case, the interest rate I ended up with was at least 1% lower than the initial offer presented to me.
After gathering the contact information for 20-30 mortgage brokers, I sent them each an email saying, in effect,
“I apologize in advance for what it will be like to work with someone like me. I am a personal finance enthusiast who is in rabid pursuit of the best deal I can find on my mortgage for the property 1234 Frugal Lane, Anytown USA. As a high earner in a very stable healthcare profession, I expect to be offered your very best rate. I also will not be paying any loan origination fees, points, or for services you can cover in order to earn my business; i.e. appraisals, inspections, etc. Your company will be competing with at least 20 others to provide the lowest rate and lowest fee option on this loan. I will be 100% transparent with you about the other offers I receive, and you will have the option to match or beat any offer. I will be taking the next 10 days to field and discuss the offers. All interested parties will have their best and final offer due on Monday the 15th at 5pm Eastern. I look forward to working with you.”
Admittedly, this has been a hectic 10 days in each instance. There are a lot of emails, phone calls, and dealing with various documents. The 20-30 contestants get whittled down pretty quickly to the five or so who want to join me in the fantasy suite of savings and who are really devoted to getting that final rose.
It’s taxing work and hearts are broken, but by my account, it has and will save me about $300,000 across those three homes. That’s a pretty good side hustle. I make a little less than $100 per hour as a financial planner, and I think I make about $10,000 per hour as a mortgage negotiator. That $300,000 in savings has been and will continue to be invested, resulting in ~$2 million of additional wealth when our current home is paid off in December 2036. It’s the Avogadro’s number of personal finance.
Fight big. Win big when and where it matters most. Don’t let those bankers capture you with their productivity-killing interest rates when the stakes are highest.
More information here:
Here’s How Much We Make, Save, and Spend as ‘Moderate Earners’
Cars
If a house is the most expensive thing we ever buy, the next most expensive things for most of us are cars. Unlike a house that typically holds its value or hopefully appreciates in value, cars do not. Over time, they depreciate to $0.
Due to the total amount we will spend on cars in our lifetime, the same Einsteinian rules apply here. The difference with cars is that the interest rate we pay for this expense should (almost) always be 0% because, in a well-functioning financial plan for a working professional, we should strive to buy our cars with cash.
This is fairly easily done with the use of “squirrel funds.” For years, I have had an automatic monthly transfer set up from my checking account to my high-yield savings account which gets deposited into different “buckets.” I “squirrel” away money for large future expenses that I know will happen; I just don’t know precisely when the expenses will show up or exactly how much they will be. I have buckets for Home Repairs/Upgrades, Healthcare, Cars, College (529s are a type of squirrel fund), Weddings, etc.
To figure out how much to transfer to the car bucket, I simply take the number of cars I will be replacing in our household (I’m not replacing the kids’ cars; they can buy their own once the high school beater dies after college), the number of years I intend to drive those cars, and the expected replacement cost. That gives me an amount to automatically transfer to my car squirrel fund each month.
We have two cars in the household, anticipate driving them for 15 years, and expect the replacement cost to be $25,000 (we buy boring, used cars). That's (2 x $25,000/15)/12 = $278 per month. Arguably, I could save less since the money is earning 4.25% (pre-tax) in my high-yield savings account but that makes the math too clunky, so I just keep it simple.
Then when it’s time to replace a car, we buy it in cash with the money already squirreled away in its duly appointed bucket.
I have written previously about how buying cars with cash and driving them for a long time is a vastly underrated way of building wealth. Paying 0% and earning 4+% on the second-largest expenses of our lives is a good way to beat the bankers. I like to believe earning interest on my car savings and not paying it warms the quarks in Albert’s ghostly heart.
Our approach to cars is estimated to result in $3.3 million more dollars over our lifetime compared to the average American’s approach to car ownership. That, along with an extra $2 million from negotiating our mortgage rates, illustrates Einstein’s’ point and shows the value of fighting/winning big.
More information here:
My 27-Year-Old Car Will Make Me a Multimillionaire
A Word About Adjustable Rate Loans
I wonder if adjustable rate loans are the most misunderstood and most underutilized financial instrument in our country. People HATE adjustable rates, and I understand why. We like certainty, we prefer knowing what the payment will be, and we enjoy the peace of mind those fixed rates offer. If that is you and you know you are paying more for this peace of mind, that is totally reasonable. But most people are not making this choice intentionally.
I believe the most rational way to think about a fixed-rate loan is to consider it as an insurance product. You are buying insurance against rising rates and transferring the possibility of that risk away from yourself and to the lender. Like any insurance product, this costs you something.
How much? Just look at the difference between what the lender is offering on an adjustable rate vs. a fixed rate. For example, a 10/1 ARM is an Adjustable Rate Mortgage (ARM) that has a fixed rate for 10 years. Then, the rate can adjust based on current rates 10 years from now, and the rate can adjust once per year. It’s not unusual for the ARM to have a 1%-2% lower rate to begin with than the fixed rate. (Note, this assumes “normal” economic conditions, not the inverted yield curves we have seen the last couple of years).
As discussed above, 1%-2% on a mortgage can add up to a lot of money over time. In other words, a fixed interest rate can be pretty expensive insurance.
Jim has previously talked about how we should only insure against financial catastrophe, including death (term life insurance), disability (own occupation long-term disability insurance), liability (auto, malpractice, and umbrella insurance), injury/illness (health insurance), etc. We should not insure against anything that is not a catastrophe (scratching our cell phone screen, our refrigerator going out, travel insurance, etc).
This begs the question: is a future interest rate increase going to represent a financial catastrophe? Maybe, but probably not.
There are four things that can happen to interest rates, and in three out of the four scenarios, the adjustable rate comes out ahead.
- Rates go down: If you start with 5% instead of 7% and rates go to 4%, you win (and, as a bonus win, you don’t have to pay five figures to refinance your mortgage).
- Rates stay the same: If you start with 5% instead of 7% and rates don’t change, you win.
- Rates go up slowly: If you start with 5% instead of 7% and rates slowly climb to 6, 7, or 8% after your rate adjusts, you win. You win because you have been paying a lower rate for some period of time and the principal on which you are paying a slightly higher interest rate in the future is on a lower balance which still results in an overall win.
- Rates go up quickly: If you start with 5% and rates rise quickly to 9% or 10% after your rate adjusts, you likely didn’t win. You will have wished you had a 7% fixed rate.
What if you are on board with the logic described here and are considering an adjustable rate but you are worried about that fourth situation? The key is to determine if you can afford the worst-case scenario. In other words, is the worst possible outcome actually a financial catastrophe, and, thus, do you really need this insurance product (the fixed rate)?
When it comes to ARMs, you will see in the loan document how much the rate can increase each year and what the maximum rate can be. You’ll see products described like this: 7/6 ARM 3/1/5. The first number refers to how long the rate stays fixed at the beginning of the loan—in this case, it's seven years. The second number is how often the rate adjusts after the fixed period—every 6 months.
The last three numbers listed are the caps and floors. In this case, your rate won’t go up or down more than 3% on the initial adjustment. The rate can’t increase or decrease more than 1% with each adjustment after the first. Finally, your rate won’t rise or fall more than 5% over the life of the loan. Make sure you know all your interest and payment caps when considering an ARM.
Do the math and ask, can I afford the house payment at 11% and still reach my goals? Or, if the rate adjusts to a problematic level, am I willing and able to cut other expenses to compensate?
If you didn’t buy “too much house,” you may be surprised to learn that the answer is yes. Thus, no catastrophe and no need for interest rate insurance. If the answer is no, buy the insurance and get the fixed rate.
Ultimately the decision is up to each person, and how we all value peace of mind will result in different “right” answers. There are no wrong answers, and the mathematically right answer will only ever be knowable in hindsight. My invitation is simply to make this decision—and every decision—intentionally.
TL/DR
- Context is everything. Put the decision in context and let us devote our ever-dwindling executive bandwidth in proportion to the actual impact of the decision.
Don’t fight small. Bask in the sublimity of simplicity. - Go hiking with your loved ones, and occasionally indulge in the Chandelier Bars of life. Don’t chase small (1%-2%) interest rate differences on your cash.
- Feel free to pay off that mortgage instead of sitting on cash. It will feel so good, and if you regret it, let us know because you are likely the first.
- Cancel all but one or two of your credit cards. No one ever got rich saving an extra 3% at Lowe's.
- Fight big. Win big. Harness your Brownian motion for the contexts when it really matters.
- Be the most annoying, intransigent person to ever purchase a home in the history of mankind. Make sure mortgage brokers are screenshotting your conversations and making fun of your insanity with their other broker friends.
- Other than a house, don’t buy stuff you don’t have the money for. Save up the money, let it earn interest on your behalf, and then stick it to the bankers who are looking to ensnare and repress you with their interest rates.
- Fear not the adjustable rate; it turns out in your favor more often than you may realize. You may not need the insurance product that is a fixed rate loan.
- Learn about how time can never be linear in the presence of gravity and feel all your cares slip away across the event horizon of the space-time continuum.
How do you use interest rates to your advantage? Are there other times when interest rates matter and when they don't? What are your thoughts on ARMs?
Great article,
one other ARM mortgage scenario
I am retired now but always loved the 7 year ARM mortgage. I worked for a fortune 500 Company (not a physician) and early in my career would relocate every 4-6 years. So….
if you know you are going to move / upgrade or sell your home in less than 10 years and have a 10year ARM, you also win!
Thanks for taking the time to read and comment Tom.
I agree that the ARM has great value when the expected time in the home is close to time when the rate adjusts. It is weird to me when people say “This is just our starter home, once we have kids in 3-7 years we will definitely need something bigger and in a better school district. We got a 30 year fixed rate mortgage for 7% because we didn’t want the uncertainty of a 7/1 ARM at 5%.”
We were in our first house 4 years, our second house 6 years, and this is year 3 in our third house. In each case we thought it was our “forever home”. I see a lot of clients spend ~3-10 years in their “forever home” who would have been much better off with an ARM. Life changes fast and it’s shockingly hard to know anything about what our future self will be like and want 5+ years from now.
On the other hand, we’ve owned two homes that we knew were not our forever home and one that we thought probably was, and have been in that one for 14 years and still can’t imagine leaving it before we are forced to. Sometimes forever homes really are for ever.
Yeah, it’s hard sometimes to know which home will really become the forever home, I have seen many clients choose to make the starter home the forever home.
First, I love your house too. Your house is awesome and I wouldn’t want to leave either. Great view, quiet street, super close to the canyon for ski access….those three things alone are “forever” qualities for me.
Second, as it relates to the ARM conversation, I believe you paid off the mortgage in 2017 which I think is about 7 years after you bought it. This means a 7/1 or 10/1 ARM would have likely worked out well for you guys even in the forever home as you never would have experienced the rate increase (obviously please feel free to correct me and/or add additional insight and context).
https://www.whitecoatinvestor.com/were-debt-free/
A 7 or 10 year ARM would have worked (we had a 15 year fixed that was refinanced twice) for sure. Although I’m not sure we knew we’d pay it off in 7 years when we bought the home.
Great article Dr. Scott! You covered many interest rate situations. I enjoyed reading about each. My wife and I did a 7/1 ARM because we got a better rate. We ended up paying off our mortgage just prior to the adjustment period (7 years). On a different note, what are your thoughts on credit card churning? For example, many cc offer a welcome bonus (60,000 points = $600-$95 annual fee = $505) for spending a certain amount of money ($4000 is typical) on the cc within 90 days. The dollar profit per welcome bonus is little, however, the return on investment is 12.6% ($505/$4000) and takes maybe 1 hour of my time to find a cc and fill out the application. Thus, my hour of time equates to $505. Thoughts?
Two thoughts from me:
# 1 Do you need the money? I’m guessing not if you paid off a mortgage in 7 years.
# 2 Is your time worth more than $505?
Early on I did a few things like this. Now looking at it from the back end of being FI it all seems kind of silly.
Thanks for sharing your ARM success story 💪!
My thoughts about credit card churning – Sounds like a hobby you enjoy. Some hobbies cost money (mountain biking), some hobbies cost nothing (hiking), some hobbies pay a little (playing in a local band or credit card hacks). None of these things change the arc of someone’s financial life.
I hate dealing with the applications, technicalities, and cancellations of various credit cards. That hobby is not for me and I don’t need $505 to reach any of my goals so count me out for credit card churring. You may rather do anything than come hike Mt. Olympus with me on a fall morning and be much happier at home finding the next card to optimize. That is wonderful and part of what makes us all interesting and diverse.
Neither my hike nor your credit card hack is going to make any difference for either of our financial lives.
I must be doing the wrong hikes if it’s supposed to be a free hobby!
Thanks for your thoughts. Credit churning is something I enjoy now, but I know my joy of it will fade. I actually like the outdoors and would choose a hike over credit card churning any day. I am a big fan of exercise and being active. Having run hundreds of road races, including 19 marathons (eg, Boston, New York City, Chicago, etc,), I encourage people to be active. Thus, if a person had to choose between an hour hike or credit card churning, I say pick the hike. Your point is well taken, time is limited so spend it well.
Nice article, but I have one quibble: Avogadro’s Number, named after Amedeo Avogadro, predates Einstein by arguably several decades.
which is presumably why it isn’t named after Einstein but instead Avogadro!
@Nerdy Chemist and @Jenn. You are overlooking the fact that Avogadro never knew “his” number. He came up with the postulate that similar volumes of gas at the same conditions had the same number of what we now know as atoms and molecules. The number involved was not called Avogadro’s Constant until after his death and it was not well calculated before Einstein’s work on Brownian motion published in 1905 which then also confirmed the atomic hypothesis. It was first called “Avogadro’s Number” by Perrin in 1909 and Perrin was drawing directly on Einstein’s work as well as other methods to calculate the number we teach in chemistry classes today. Tyler’s writing is such a delight that I don’t even worry about that fact that there is no direct evidence Einstein ever said anything about compound interest. (Tried answering with links to some papers but that triggers a review and maybe rejection.)
Here’s a link: https://skeptics.stackexchange.com/questions/25330/did-einstein-ever-remark-on-compound-interest
It seems unlikely Einstein ever commented about compound interest.
Avogadro didn’t calculate the number and it wasn’t so named until 1909 after Einstein’s 1905 work. Avogadro came up with the idea that a volume of gas would be proportional to the number of atoms or molecules regardless of what kind of molecules were involved. First estimates of the number I think came well after his death. Einstein’s work on Brownian motion led to a way to calculate the number and ultimately a confirmation of the atomic theory. (On the other hand, Tyler’s writing is so entertaining that my mind doesn’t want to go to that dark place where there is no evidence of any direct statement by Einstein on interest rates.)
https://en.wikipedia.org/wiki/Avogadro_constant
https://www2.math.uconn.edu/~gordina/Measuring%20Avogadro%27s%20Number%20Using%20Brownian%20Motion.pdf
https://research.chalmers.se/publication/528592/file/528592_Fulltext.pdf
Mortgage Payoff vs. Cash:
Cleanup No. THREE: Money market rates will (probably) soon be dropping, Vanguard’s already has by a bit from 5%. The mortgage is fixed until paid off, even when money markets are pnly paying 1% again. Now if you could put the money in a fixed rate CD or bond you won’t need to access early- ok not your emergency fund then.
I doubt they’re going back to 1%, but 5% doesn’t seem to be very sustainable either. They haven’t spent very many of the last 25 years over 5%. So a guaranteed 5-7% paying down debt becomes attractive again.
Yes, good point Jenn. The biggest point I’m try to make is that is just doesn’t matter in a meaningful way regardless of what the money market rates are.
If you want to keep cash, great, keep cash. If you want to pay your mortgage off, great, pay it off. Both are good, both are right, both represent a choice that will lead to victory because they both support a net savings rate and at the end of the day savings rate is the only financial variable that really matters that is within our control.
Ah, Dr. Scott. One of my favorite WCI Columnists because he is surely one of the funniest. This was a great read. Thank you for writing it. I’m going to send it to my family and friends, all of whom will sadly ignore it. Speaking as someone with over 20 credit cards, however, I must point out that the only sane reason for such a strategy is when the cards earn points rather than cash. We have traveled the world in the front of the plane and stayed in some awfully nice hotels for insanely small amounts of money. It’s a fun hobby for those who find travel optimization fun. 🙂
I actually like cash back. It’s like a 1-5% discount on everything I buy all while paying for it in the most convenient way possible. Yea, maybe I could do better by juggling 20 credit cards and their sign-up bonuses, but that seems like a lot of hassle.
I hear you WCI! I’m just one of those weirdos who find it calming and fun to keep a spreadsheet on all my credit card info, so for me it’s (usually) not too much of a hassle. Hope you’re well. It’s especially nice to get another response from you as I’m in Salt Lake, about to head out to do one of my 4x per year events at the IMH Leadership Institute. Chilly here!
I love this hobby for you. Truly, it delights me when I see someone’s eyes light up describing their travel points passion projects. We were these people once and flew to Thailand in business class for “free”, it was awesome.
I say “free” because, well, it’s not free. It costs a ton of time and energy to be totally on top of all the cards, their annual fees, the minimum spends, the transferability of the points, etc. To you and people of your ilk, this is time well spent and a hobby you love. That part I have no quibble with.
The part that I see missed in this conversation is the “We have traveled the world in the front of the plane and stayed in some awfully nice hotels for insanely small amounts of money” part of the story. I totally believe you that the amount you paid out of pocket is minimal for these awesome experiences.
What I wonder is: What is the difference between the retail value of your travel and how much you would have earned in cash back?
When I have done this math for myself and for clients, the answer is “very little”. In other words, if over a 3 year period I got 2-5% cash back that equals $20,000 and I see the value of my travel points have offset retail travel costs that otherwise would have been $22,000, then all my work and hassle during those 3 years was worth $2000.
Cash is the ultimate gift card. I can use that cash back on a new car, a home repair, or on travel. The “points people” can only use it on travel and its net value is just not that compelling in most cases. Exceptions are when people travel A LOT. In those situations the travel points/perks can be meaningful but for most people with 10 days of PTO a year, these travel rewards are overstated and overrated.
That said, if the points “force” people to travel when they would not have granted themselves permission to travel otherwise, I think that has value too.
If you disagree and have trackable/shareable data, please consider writing a guest post on the profound financial life changing value of travel points OR just on the shear joy it brings you even if the math isn’t so profound.
Thanks for your reply. I love the idea of writing a guest post! Perhaps I’ll do that someday. Two points you make at the end of your response are especially important here.
1. “Exceptions are when people travel A LOT. In those situations the travel points/perks can be meaningful but for most people with 10 days of PTO a year, these travel rewards are overstated and overrated”.
2. “That said, if the points “force” people to travel when they would not have granted themselves permission to travel otherwise, I think that has value too”.
These are excellent points, and the first one makes me realize how lucky I am.
First of all, I’m a tenured professor, so I have much more time available for travel than most. Because I run a large research lab, my time is never entirely “free”, but summers and holidays provide ample time and flexibility (around 4 months/yr) for travel. I’m also self-employed as a consultant and professional speaker, so that involves a fair amount of travel, too. You are right that people with only 10 days of PTO each year are unlikely to benefit in the same way. But for me and my family, we are able to get an extraordinary amount of value from the points hobby.
Your second point, about “forcing” people to travel and have experiences they otherwise wouldn’t, is also germane here. For example, I would NEVER pay $22,000 for a first class ticket to Italy, but that’s exactly what my wife and I did for our honeymoon in 2016 . Except we paid around $1000 each for the same ticket on Emirates (the plane with the showers!). We were even able to build a free stopover in Dubai where we spent a few days doing things like riding camels in the desert before heading to Tuscany for 2 weeks. It was a once in a lifetime experience, made possible with Alaska miles and a comparably small outlay of cash. Importantly, it didn’t take 3 years to build up the points that allowed these tickets; it look less than 1. That’s just one of many examples of incredible and otherwise out of reach experiences we’ve had because of the points and miles game.
Now, I can hear WCI chiming in to ask me about the value of my time, and how much time I spend on this hobby. Fair enough. Over the years, I have developed good systems and spreadsheets that minimize this, but yes, there is time involved. For whatever reason, though, I really love the hobby, so I consider it time well spent — especially because I don’t see how cash back cards could quickly provide the money needed for these sorts of awesome trips. And we take a lot of them.
You’re right that cash is the ultimate gift card, and the flexibility of cash is likely more important to many people. But knowing myself, I would simply invest that cash. Whenever I have cash, I can’t help but immediately put it to work in the markets, whereas having money in the form of miles “makes” me spend them on wonderful family travel experiences.
I’m grateful for that because we wouldn’t do it otherwise. I hope this perspective helps.
Phenomenal response! I love this so much and really appreciate you advancing the conversation.
What I hear in you is – Self Awareness and Intentionality.
Awareness – You know yourself, your behaviors, your values. That is such an important place to start a financial journey from.
Intentionality – You are doing this on purpose, for a purpose, and you know what you are trading to get it. Intentionality is such a powerful corollary to satisfaction in any part of life, especially finance.
Please consider writing that guest post!
Thank you for this response. Given how often I’m in Salt Lake City, I’m strongly considering giving you a call for help (probably a limited review) given my plans for a possible early “retirement” from academia. 🙂
I’d be happy to help, feel free to reach out if/when the timing feels right. Congratulations on the path to early retirement.
Enjoy your time along the Wasatch Front, hope you earn some quality travel points while you are here!
https://www.whitecoatinvestor.com/contact/guest-post-policy/
Your posts are really insightful and I really enjoy your humor! I reached the same conclusions myself regarding ARM mortgages and credit card points. Funny how obvious things don’t get the attention they deserve and vice versa.
Thanks for reading and for the kind words.
Yeah, it is wild to me how things with a 1 or 2 out of 10 impact get a 9 out of 10 level of attention and discourse. Conversely, many things with a 7 or 8 out of 10 impact get relatively little focus and “hype”.
Perhaps a future post will try to categorize the impact/controllable elements of a financial plan; low-impact with no control, high-impact with no control, low-impact with control, high impact with control. Our attention should be disproportionately focused on this last group – high impact with control .
Love this post! Excellent points + hilarious! I actually laughed out loud reading a finance blog, now that’s something. Since many of us over- research each financial decision, focusing on high impact decisions is great advice. More from Tyler please!
Thank you for the kind feedback and encouragement to keep writing for WCI.
I agree with you that many readers here are likely “over optimizers”. I love the over optimizers because the nerdiness of the discussions brings me so much joy. It also reminds of the dangers of living in that world too often and what forests can be missed when looking so rigorously at every tree.
I have found so much value and liberation in identifying which decisions have large, moderate, mild, or no impact and allocating my attention proportionally. Knowing what matters and what doesn’t is perhaps the greatest evolution in my personal financial journey.
I really enjoy your writing, Tyler, and can’t wait until you publish a book or two. I think a common theme in the points you make on when interest rates (or differences in interest rates) do or do not matter is the length of time over which they are acting. We know from looking at compound returns for mutual funds that even a 1% absolute difference in fees, as pointed out by Bogle, can make an enormous difference over 30 years because you are compounding that small difference over the entirety of the fund each year while Dave Ramsey rightly points out that if eliminating debt quickly even large differences in interest for which debt you pay first using his snowball method as opposed to the avalanche method is not a large sum in absolute terms. Compounding is not very impressive when it only occurs for a few years; it needs a long series of compounded intervals to work its magic.
That is a meaningful and inspiring compliment, thank you!
Yes, time is perhaps the most profound of any variable in finance. How early do we start saving, how quickly can we reduce/eliminate debts, how long will we work, how long will we live, how long can we stay committed to a written plan, how quickly are we able to adapt, etc.
The variable of time, Einstein’s 4th dimension, is indeed one we must move through with care.
Great post. I believe the mortgage interest tax deduction is even less beneficial in many cases. Unless you already have $29,200 in deductions before adding the mortgage interest, only a portion of the interest is practically deductible. For example, say you have $10,000 mortgage interest and $20,000 in other deductions. Although you are technically deducting all that mortgage interest, you are really only deducting $800 over the standard deduction. So it is misleading to think that your effective mortgage rate = rate * (1 – tax rate).
Thanks for reading John and thank you for this important comment. I tried to make this point in the post but when I read it back I realize I could have been more clear. You have provided the clarity I intended to offer.
With the recent election results we can be pretty confident some version of the Tax Cuts Jobs Act will be extended which means understanding the nuances of the standard deduction and the itemized deduction will be important for the next ~10 years.
Thank you for highlighting this point.
Love this article. One of the best published in a while.
Yield chasing except on mortgages and cars is not one of the big financial rocks to focus on and distracts from the goal of getting your savings rate as high as possible. Couldn’t agree more with the premise.
I got my mortgage in 2021 with a 7 year ARM for 3.25%. My only other options were 5yr ARM (3%) & 10yr ARM (3.5%). In retrospect I should have chosen the 10yr ARM as we love the house and the job and interest rates went up significantly. On the other hand, the 7yr ARM has motivated me to pre-pay the mortgage significantly to eliminate some interest rate risk so hopefully will be on track to pay off the mortgage in 7 to 10 years instead of 30 years.
Thank you for reading, commenting, and providing the positive feedback. It means a lot to me.
Savings rate really is everything. All the strategies, mechanics, and optimization are fun and certainly valuable as a whole but even when bundled together, they all pale in comparison to savings rate. This can’t be said often or loud enough in my opinion. Thanks for highlighting that point.
Dude dominating post as usual man! I would have to fully disagree with the last point though: time in the presence of gravity can be linear just as long as both observers are experiencing the same amount of gravity. Theory of relativity my man theory of relativity!
Actually, I could really really be wrong about that.
I could be wrong also about my hobby of having over 20 credit cards chasing reward points and bonuses. I do find it a fun hobby and I think the amount of time and mental energy I spend on it is minimal with a huge payoff. It’s just so easy to open a credit card, get whatever bonus for spending whatever amount of money that I was going to spend anyway, and then use that credit card whenever it has maybe a rotating category to take advantage of 5% cashback for those three months. Definitely much easier than trying to hack travel rewards.
Again great article dude!
Thanks for always reading and being such a great hype man Rikki! I appreciate your positivity and support so much.
Regarding relativity – This is an area of interest for me, not expertise, so I defer to the physicists to correct me often in these conversations. I agree with you that the passage of time is experienced the same for two entities under the same gravitational force (their relative experience is identical per the theory of relativity).
The concept I’m referring that first blew my mind is broader and in reference to gravitational time dilation as part of general relativity. Simply that time itself is subject to gravity. If an atomic clock is placed at the bottom of the Mariana Trench and another is placed at the top of Mt. Everest and we go fetch them a year later, the one at the bottom of the ocean will have documented less time passing than the one at altitude. The higher gravity closer to the center of the earth means less time actual time passed. That is wild to me. Also humbling and fascinating and terrifying in a way that brings perspective to after-tax yields on interest bearing savings accounts.
Regarding credit cards – I’d love to see you write on post qualifying the value of this over a 12 month period. How much total time to you spend opening, closing, coordinating, and monitoring the cards? What is the total in annual card fees that you pay? How much more , if any, do you end up spending to hit minimum spends or at specific vendors/sectors that you would not have otherwise? What is the positive delta compared to a single cash back card? How does that net impact of time and dollars compare to working one extra shift? How does that net positive delta impact your long term projections and/or what financial goals are you able to accomplish that you otherwise would miss or delay without the credit card optimization?
I’m sure you could think of many other quantifiable areas to examine and articulate. It would be really interesting!
Tyler,
Have you been successful with a lender actually waving origination fees and appraisal costs?
I’ve been able to avoid origination fees with a no-cost mortgage.
I am 3/3 on getting origination fees waived. This has been pretty easy. I just say “I’m not paying you money for the right to pay you more money. You are going to make $xxx,xxx dollars in interest on this loan, if you want to lose my business over $xxxx in fees that is a choice you will have to make within your business model. I am 100% certain I can find someone else who will make a difference choice.”
I am 2/3 on getting the appraisal and inspection fees waived. The one time I paid I did it on purpose because we were buying in a frenzied market so we actually had the inspection and appraisal done before offering on the home so we could “waive inspection and appraisal” as part of our offer to make us more competitive (it worked, we “won” the house out of 15 bids even though we were not the highest offer).
I am 1/3 on getting the title fees waived/paid for. This is much harder in my experience as different states have rules about who can/cannot pay for these.
The key is to make sure they don’t raise your rate when they waive your fees. A lot of lenders will offer to waive the fees but then try to subtly/sneakily adjust the rate.
Thanks for the reply, Tyler.
When you say “inspection fees,” are you referring to the home inspection that’s for your benefit and not required by the lender? You’ve gotten this paid too?
Yes.
My position is that I am a very valuable asset (high earner with a stable job and impeccable credit) from whom many people will be making money when I purchase a home. I am limited supply in high demand.
As such, I intend to utilize market forces (i.e. competition) to create the best outcome for me. One of the many ways lenders can compete for my business is to reduce my transaction costs.
To make sure I understand, you’ve had a lender pay for YOUR home inspection that is for your purpose only and is not required by the lender?
Are they paying it by reimbursing you at closing?