In my last post I showed how compound interest allows us to save relatively small amounts of money now, but that money grows over time to cover our retirement expenses. Today I want to dig a little further into what’s going on with the math and how, once we understand it, we can use it to our advantage.
Table of Contents
The Compound Interest Equation
In the last post when we wanted to calculate our Coast FI number we just used a compound interest calculator and punched numbers in using trial and error. In the background the calculator was using something called the compound interest equation:
A = P*(1+R/12)T*12
This equation allows us to calculate a final amount of Assets (A) based on the initial Principal balance (P) we have today, an annual rate of return (R), and the amount of time in years (T).
Note that the 12’s just turn the years into months to make the returns accrue on a monthly basis. This speeds things up a little bit, but it better reflects how things work in real life. For instance, your bank typically pays you interest monthly rather than annually.
This equation shows us why compound interest is so powerful! The larger T is, the more you amplify your rate of return. With T = 1 you get P*(1+R/12). For T = 2, you get P*(1+R/12)*(1+R/12). In other words, you get a return on your return!
Rather than punching numbers into a calculator, we could use this equation to work backwards – i.e. calculate an amount of Principal required given a desired final Asset value. We simply divide A by everything except P:
P = A / (1+R/12)T*12
Pretty easy right? Now we could plug our FI number in for A, assume a rate of return, and input the amount of time we have until retirement to know how much we’d need to have today to be Coast FI! Then it will look like this:
Coast FI number = FI number / (1+R/12)T*12
If you want you can go back to the last post and do the calculations yourself -the math checks out (within rounding errors – I didn’t go to exact dollars and cents). Don’t worry, I’ll wait…
The FI Percentage Equation
Great, now let’s re-arrange the equation slightly differently. Instead of dividing by everything except P, we’ll divide by P itself:
A / P = (1+R/12)T*12
And then we’ll flip (i.e. invert) both sides:
P / A = 1 / (1+R/12)T*12
Wait, what happened? This looks a whole lot more complicated, but it’s actually pretty simple. We just created an equation to solve for the percentage of our FI number we need to have saved today in order to reach FI by the time we retire.
Still not sure what we just did? Think of it this way – you tell me how long you have until you want to retire and the rate of return you expect to get, and I’ll tell you what percentage of your FI number you should have saved by today in order to reach your goal.
The beauty of this is that I don’t even need to know your FI number. It could be $1,000,000 or $10,000,000. Doesn’t matter. Don’t believe me? Let’s try it out using our compound interest calculator from last week. The website it’s on happens to be run by the Securities and Exchange Commission (SEC) so hopefully you can trust it. If not, you can always run the numbers on your own to verify.
Let’s say you expect a 5% rate of return and have 30 years until retirement just like last time. If your FI number is $1,000,000 then we already established that you’d need around $224,000. The exact number is just a shade under $223,827.
And if you need $10,000,000 to retire? Remember, the percentage is the same. We just multiplied the FI number by a factor of 10, so multiply the Coast FI number by a factor of 10:
Is your mind blown yet?
Introducing The Coast FI Glidepaths
If this is true, then for a given rate of return we can calculate what our Coast FI number should be for any length of time from retirement. Don’t worry, I did it for you. I present to you the Coast FI Glidepaths! ::cue triumphant music::
Oooooh, pretty!
I no longer need to know your FI number in order to know if you’ve reached Coast FI. We can divorce ourselves from dollar numbers and instead talk about how close to retirement we are in terms of time versus how far away we are in terms of money.
Got 25 years until retirement and expecting a 6% return? You should be 22.4% to your FI number.
Got 10 years and expecting 8%? You should be 45.05% of the way there.
So what are some of the things we learn from these glidepaths?
- First, the further from retirement you are, the less you need to have saved as a percentage of your FI number. These curves get steep really quick as you approach retirement age. The earlier you start the better.
- Second, your expected rate of return makes a difference, especially in the 20-40 years until retirement range. Because the curve is anchored at 100% to the right and asymptotes to the left, the “wiggle” is in the middle. Even at a 4% rate of return, if you’ve got enough time on your side, you don’t need a ton of money. Conversely, if you only have 5 years left, your rate of return won’t make too much of a difference.
- The maximum difference between the 4% return curve and the 8% return curve occurs at 17 years from retirement where they’re almost 25% apart. At that point you’d need to have almost double saved if you’re investing for a 4% rate of return (50.72%) than you would if you’re assuming an 8% rate of return (25.78%). This isn’t to say that you should necessarily aim for an 8% rate of return if you’re behind – more on that in future posts.
- If you’re on the Coast Fi path you don’t need to share your absolute net worth numbers. Sharing your percentage to FI is sufficient, if you’re inclined to share even that much. If you’re lucky enough to be saving more and not simply letting things compound, then you can think of that as reeling in your retirement date (i.e. you’ve “climbed the curve” to a spot further to the right on the glidepath).
How Should I Use This?
Let’s say you’re just starting out on your journey. You’ve started tracking your expenses and have a rough idea of how much you spend per year.
It’s important to recognize first that your progress to Coast FI doesn’t depend on the absolute amount of money you have saved, but rather on the proportion of your FI number that you have saved.
At this point you should make some projections into retirement. Maybe you plan to ball out in retirement, traveling around the world on cruise ships. Or maybe you think your expenses will decrease with kids out of the house and a slower pace to life. Whatever your plan is, figure out how much you plan to spend on an annual basis.
When will you retire?
Determine at what point you want to stop working.
There are some standard retirement ages. At 59 1/2 you can take money from your 401K. Once you reach 62 you can access Social Security. At 70 you can take full Social Security.
If you’re familiar with FI though you might target an earlier date. Just because we’re coasting doesn’t mean we have to coast to a particular end date. Maybe you’re still aiming for 55 but want to coast until then. It’s totally up to you!
Determine your assumed rate of return
What are you comfortable investing in? Are you ok with 100% stocks? Or would you rather have a 50/50 stock/bond split? Based on the investments you’re comfortable with, determine what you think they’ll return between now and when you retire.
Since you’re coasting and don’t expect to need the money soon perhaps you can be ok with a higher risk tolerance.
Don’t forget to take into account how expensive the various asset classes are that you’re invested in.
Figure out your FI number
This should be based on your expected retirement income, expected retirement expenses, and your risk tolerance. If you expect some reliable retirement income (e.g. you have a strong pension) then your FI number should be lower. If you have a lower risk tolerance, you’ll want to use a lower withdrawal rate, which would increase your FI number. Maybe you’ll want to factor in some large expenses like long-term care.
Calculate your Coast FI percentage
Now that you know everything above, you should be able to calculate what your Coast FI percentage is. Use your time to retirement and expected rate of return to calculate your Coast FI percentage. Calculate what you currently have saved divided by your FI number.
If what you currently have saved as a percentage of your FI number is larger than your Coast FI percentage then, if your assumptions are correct, you should be able to take your foot off the gas. Slow down. Enjoy life more. Take some more vacations. Switch jobs if you’re unhappy.
If what you have saved as a percentage of your FI number is lower than your Coast FI percentage then you can figure out how long, based on your savings rate, until you reach your Coast FI percentage (more to come on this). You’re not there yet, but if you’re catching up to these glidepaths, then you’re on the right track.
Gut check your assumptions
How aggressive are you being? Perhaps you should err on the conservative side to be safe. After all we are likely projecting a long way into the future.
The longer from retirement we are, the bigger those error bars get. We don’t want to find out 20 years from now that we came up short because our assumptions were too aggressive.
You can bake a little conservatism into one or all of these numbers if you want. In fact, you should play with a range of assumptions for each to get a feel for how solid your forecast is.
How Will You Use the Coast FI Glidepaths?
So there you have it, the Coast FI glidepaths. I believe they’ll become a really useful tool for folks who are interested in Coast FI to easily assess and measure their progress. As I’ll talk about in the future, they’re also a great tool to help check in periodically on whether you’re still on-track.
What do you think? Will you be able to apply them yourself? If so, how? I’d love to hear about it in the comments!
Cover photo: Teacher’s hand writing complicated mathematical formulas on the whiteboard by Marco Verch under Creative Commons 2.0
