My 2021 savings will pay for my lifestyle in 2040, 2059, and 2078 (if I’m lucky). And your 2021 savings will pay for your entire lifestyle in future years. This article will show you the math.
Kinda cool, right? The choices I make now will directly pay for my lifestyle during specific future years. Next year’s savings will pay for the next future years’ spending. The pattern repeats itself year after year.
The challenging part of this idea is the math. You want to answer, “What future year can I start planning for? When can I retire?”
Read on and find out.
What About the “4% Rule?”
Yep, I think the 4% rule is great. If you like the 4% rule, use it.
Today’s idea is parallel. It’s a related mental model.
Saving Now – 2021
I’m trying to save ~40% of my income this year. I will spend the other 60%. That 60% covers taxes, normal expenses, fun stuff…everything. You’ll need to remember these two numbers. 40% savings and 60% spending.
I’ll deposit those 40 % savings into an investment account and let it grow.
Next, let’s assume a conservative 5% annual real growth rate (real = adjusted for inflation). And then we’ll fast forward to 2030. That “40% of my income” has grown! After 9 years of 5% growth—40% * (1.05)^9 = 62%—the initial 40% is now worth ~62% of my annual income.
As you recall, my spending is 60% of my annual income. In other words, the saving I do in 2021 will grow and then pay for my life in 2030!
My 2022 savings will then pay for my life in 2031. And 2023 will pay for 2032. One year of saving will pay for a future year’s living. This is magical.
So…should I retire in 2030 and start living off past years’ savings?
We Hit a Snag and Stall Out
We’ve confirmed that each year in the 2030s will be funded by the savings from the 2020s.
But what about the year 2039? You sharp mathematicians might notice an issue with that year.
Can you spot it?
The year 2039 should be funded by my savings from 2030. But did I save in 2030?
No! I did not! 2030 was my first year of “retirement,” where I spent all the money I had saved from 2021. The 2021 money had grown, but only enough to cover my 2030 spending (~60%). I had nothing left over from 2030 to save for the future.
We’ve hit a snag. This initial plan only saves enough for one year of future spending. I saved for nine years, spent for nine years…and then stalled out. I would find myself in 2039 will no money leftover.
If I plan on living past 2039 (let’s hope!), I need to adjust this plan. My savings from 2021 need to do more than fund a single year of future retirement. Instead, they need to fund one year of retirement and then leave leftover money to keep growing.
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But How Much Leftover?
How much leftover is needed each year? The math is simple!
In my first year of retirement, I’ll require one year of spending (60% of my income) plus enough leftover to restart the cycle of growth. How much leftover? The same amount I initially started with. That’s easy—that was 40% of my income.
I need enough to spend 60% and have 40% leftover to start again. That’s 100%.
It’s a cycle of money. The cycle starts with saving 40% of my annual income. That 40% grows until it eventually becomes 100% of my annual income. The cycle ends with me spending 60% of that money while simultaneously restarting the cycle with the leftover 40%.
For this scenario—assuming a 5% real annual growth rate—I require a 19-year cycle to grow the initial 40% of my income into 100% of my income. [40% * (1.05^19) = ~101%].
If I were to start from scratch today and save 40% of my income each year, I could retire in 2040.
So let’s fast forward to 2040 and see how it would work.
The money I save in 2021 will fund my 2040 spending and will leave money behind to keep growing. That leftover money will grow to fund my 2059 spending and will leave behind money to keep growing. That leftover money will grow to fund my 2078 spending and leave behind money to keep growing. Etc. Etc.
2022 will fund 2041, 2060, 2079, etc.
2023 will fund 2042, 2061, 2080, etc.
2040…will be funded by 2021 and there will be leftover money to fund 2059, etc.
Retirement is nothing but a cycle of money, today’s dollars growing into tomorrow’s living expenses.
How Do I Calculate My Cycle of Money?
There are a few ways to calculate the timeline of your cycle of money.
Below you’ll find:
- A graph to investigate
- And the governing equations
You can find the length of your “Cycle of Money” however you’d like. Here’s the governing equation:
Length of cycle (in years) = LN(100%/[Pre-Tax Savings Rate]) / LN(1 + Real Rate of Return) where LN is the natural log function.
For example, my scenario from above is: LN(100%/40%)/(LN(1+5%) = 18.78 years.
After 18.8 years, I can retire and start my Cycle of Money!
If I assume the historical average stock market return (7% per year after adjusting for inflation), then my 40% annual savings means I can retire in 13.5 years.
If I save 50% of my income and assume a 7% investment return, I can assume in 10 years. Cool stuff!
Whoa! What Assumptions Are We Missing?!
Yes, there are important assumptions here. For example, it’s not wise to plan a full retirement from a 1200-word blog post.
Age restrictions – if you’re saving in a Roth IRA or 401(k), you have to wait until age 59 to withdraw that money penalty-free. Look at Roth conversions, though. Many early retirees use them.
If you’re saving in a taxable brokerage, you’ll have to pay capital gains taxes when you withdraw that money. But keep in mind—I am counting taxes in my 60% spending numbers. Thus, the tax assumptions I’m making shouldn’t be too different from reality.
Raises? Spending changes? I’ve assumed a constant lifestyle—spending, saving, and salary all increasing by the rate of inflation. That’s not one size fits all. Want to be smart? Your saving should grow faster than your spending.
Social security. I didn’t count social security in any of this math, despite the fact that I’ll have access to it at age 62.
Retirement planning is more than just one number. It’s complex. But this “cycle of money” should help you visualize why today matters so much.
There’s a one-to-one connection between today’s savings and a future day’s retirement. The more you save, the quicker that future will arrive.
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