Mental Models: FI Math
A few weeks ago, I talked about the importance of mental models to leveling up our problem-solving abilities. I came across an article in the Washington Post yesterday that happened to be about the UK coronavirus variant and its increased reproduction rate and I thought it was a perfect example for the FI Weekly.
My bringing this up here isn’t necessarily about coronavirus, but the increased level of understanding we all have when we understand exponential math, the math behind the compound growth of our money, and mental models generally.
The article noted that in a Facebook post, the Danish “Prime Minister Mette Frederiksen told people to imagine sitting in the top row of Copenhagen’s Parken Stadium, a soccer arena with a capacity of 38,000 people. A dripping tap is filling it up, one drop the first minute, two drops the second, four drops the third. At that rate, Frederiksen said, the park will be filled in 44 minutes. But it will seem almost empty for the first 42 minutes, she said. “The point is, you only realize that the water has risen when it’s almost too late.””
When you work backwards with it doubling every minute, the stadium would be 50% full at 43 minutes, 25% full at 42 minutes, 12.5% at 41 minutes and a mere 6.25% full at 40 minutes.
At minute 35, at less than 0.2% full, it would be impossible to predict the tsunami of water coming your way unless you had an understanding of the math.
This reminds me of the doubling of our money, the “Rule of 72”, and how small differences in return (or reproduction rate of a virus, etc.), can make massive differences in the final outcome.
The ‘Rule of 72’ states the number of years to double your money is equal to the number 72 divided by the rate of return on your investment. For example:
If your return is 6%, your money doubles every 12 years (72/6 = 12 years)
If your return is 8%, your money doubles every 9 years (72/8 = 9 years)
Let’s look at the impact on a 30-year-old with $100,000 saved up (assuming no additional money invested):
6% return, doubling every 12 years:
- At 42 they have $200,000,
- 54 years old: $400,000
- 66 years old: $800,000
8% return, doubling every 9 years:
- At 39 they have $200,000
- 48 years old: $400,000
- 57 years old: $800,000
- 66 years old: $1,600,000
Starting from this “small” difference of 2% return in the first year, which would amount to just $2,000 that first year, it ultimately led to the person with the 8% return having double the money at 66 years old.
Rate of return matters. Reproduction rate matters. Understanding the underlying math matters a great deal.
Back to Basics: Banking Edition
On a recent ‘back to basics’ podcast episodes, we talked about the importance of setting up your banking life in a comprehensive, yet simple and easy to use manner. Our team produced an amazing companion article that I think you’ll get a lot of value from entitled “Banking 101: The Ultimate Guide to Banking Basics in 2021.”
If you aren’t happy with your current banking setup, or you want a refresher on ways to optimize, this article is the place to start:
ChooseFI Community Taking Action This Week
- Karen said, “After hearing Poliygenius ads for years on various podcasts, I finally took the service for a spin, and saved $618 (25%) on my annual insurance premiums. I had to do zero work — they found the cheapest comparable packages, reviewed the options with me, signed me up, AND notified my previous insurer that they’re getting the heave-ho!”
- Jake said, “This week I have 2 wins: 1) I am a firefighter and I received my second dose of the vaccine yesterday. While I am still feeling a little groggy and not as energetic as usual, it is great to know we are on our way back to seeing friends, traveling, and getting the kids back in school. 2) My mom called me out of the blue yesterday and said she was finally ready to leave her broker at Edward Jones. (I have been trying to explain how much she is paying for a couple years now). She said she sold some stock lately and realized they charge her 2% each time she buys and sells stock. I was able to send her to M1 finance so she can buy both index funds and have fun picking individual stocks. Thanks for the recommendation, Jonathan!”
- Renee said, “This week I maximized my 401k to 17% in order to hit the max contribution for 2021! I also have a plan to max out my Roth for 2020 (before the April deadline) and for 2021. I’m 44 and I always contributed to my 401k but never maxed it out. So, this is a huge step and I’m so excited to see my numbers grow!”
- Caroline said, “My 1% is on health optimization. I really enjoy running tests on my body to better understand what’s going on and detect trends – what can I say, I am a numbers person! So, I decided to use my bonus to do an at-home food sensitivity test through Everlywell. That was my treat; I saved all the rest! To my surprise, it showed I had medium sensitivity to 3 things I’ve been eating all my life (milk, yogurt & egg whites). I decided to give it a try and cut those 3 items from my diet. After a few weeks, my persistent post-40 skin issues disappeared and I feel more energy than ever! That, paired with my intermittent fasting which I’ve adopted 2 years ago, improved my overall health by a lot! It wasn’t easy to replace the items, but I am always eager to learn and change to have better quality of life.”
- Brandon said, “For my 1% better I finally opened up a Vanguard account and am investing for my future. My second job that I only work 2 days a week ends up paying the bills (cheap rent in my low cost of living area) therefore my “main” 9-5 job ends up all being supplemental income. I am 23 and am beginning my path to FI with this being my first step! (Been a crazy ride being thrown into the job market out of college amidst a pandemic). Thanks to you guys I have been able to apply actionable tips to my life to begin my path to FI at a young age where I do not have tons of expenses!”