Classical FI
Hint: it's all about your savings rate
The classical approach to financial independence (FI)
Mr Money Mustache (MMM) popularised the âshockingly simple maths behind retirementâ back in 2012, and itâs generally seen as the âclassicalâ way to become financial independent (FI).
Classical FI doesnât care about ratios between pensions and ISAs, about whether youâre LeanFI or FatFI (yes, those are apparently things), or what age youâre thinking about retiring. Itâs a really simple way to let you know when you can retire.
To quickly recap, financial independence, is a state where you have enough wealth to live on, or assets generating enough income, such that you donât need to work a ânormal jobâ anymore.
As long as youâre investing your savings, and getting a decent interest rate
, theyâll grow and eventually generate enough returns that you can live off the returns alone. At that point youâre financially independent and can stop working if you want.
The percentage you withdraw every year should be slightly less than the interest youâre earning, known as a safe withdrawal rate (SWR)
, that way the money shouldnât run out, and youâve got a little margin for poor performing years.
Savings rate is key, not the absolute numbers
MMM explains that the absolute numbers (how much you earn, and how much you save) arenât as as important as your savings rate
which = amount you save / amount you earn after tax
.
To illustrate why, here are the two extremes:
- Save 0%, and spend 100% of your income, youâll never save a penny, and youâll have to bank on the state pension at 60something (or more likely 70something) when you eventually retire
- Save 100%, and spend 0% of your income (i.e. live for free) and you could stop working and retire now (assuming you can maintain this lack of spend if you stopped working)
If your savings rate is somewhere in the middle, youâll become financially independent somewhere in the middle too. Hereâs a chart that shows a little more - years to FI vs savings rate.
A higher savings rate accelerates the time to FI
This chart below shows that the time it takes to get financially independent does not scale linearly with your savings rate.
The beauty of having a higher savings rate is that youâre not only saving more money, faster but youâre also spending less, and need less money overall to retire. These two things have a compounding effect, and can rapidly accelerate financial independence. Thatâs why the graph isnât linear, itâs exponential.
What does this mean for you, in practice?
This grid, for UK audiences, is appropriated and adapted from this one by US-based Four Pillar Freedom.
It tells you, for each post-tax income (the x-axis) and spend (y-axis) combination, how long itâll take you to retire (in years).
The assumptions Iâve used are:
- 3.5% interest rate (above inflation) on savings
- 3.0% safe withdrawal rate (see end of article for references on why)
- ÂŁ0 initial savings
If you already have some savings, ping me an email and I can send you a spreadsheet that will let you factor this in.
Itâs all about widening the gap
The key thing this chart should tell you is that the wider the gap between what you earn and what you spend, the quicker you can retire. Exponentially quicker in fact.
For example, if youâre in the ÂŁ35k to ÂŁ45k post-tax region, spending ÂŁ15k a year vs ÂŁ30k could mean you retire in 13 years rather than 35 years. Thatâs an enormous difference.
If youâre starting at 25, thatâs retirement at 40, not 60 . Those are some peak years.
Read on for some mathsâŚ
How does the maths work?
Iâve dug into this to understand more.
We want to work out how long will it take to become financially independent (FI) for different savings rates. Letâs call this time period ânâ.
Financially independent means your expenses are covered by the safe amount you can withdraw from your âfutureSavingsâ. So weâre going to write an equation that helps us to find ânâ when the futureSavings have grown big enough to support a withdrawal rate of 3% that covers your expenses.
There are six key variables
startingPot: ÂŁX,000
interestRate: 3.5%
withdrawalRate: 3%
annualIncome: variable
savingsRate: variable
futureSavings: variable
Equation 1: your future expenses
FIExpenses
= how much youâll spend per year when youâre financially independent.
Withdrawal rate
= how much of your savings pot youâll be safe to withdraw per year
FIExpenses = withdrawalRate * futureSavings
Weâll assume youâll spend the same in retirement as you will now. So FIExpenses = currentExpenses
currentExpenses = withdrawalRate * futureSavings
Our current expenses are also a function of our savings rate:
currentExpenses = (1 - savingsRate) * annualIncome
Equation 2: your future savings
After n years, your savings will be a combination of the pot of money you started with, and the money you saved along the way (a function of your savings rate). Both of these will be growing with a particular interest rate.
futureSavings after n years = [Starting pot after n years] + [Ongoing monthly payments after n years]
We can calculate how the starting pot will grow, using a compound interest calculation. Weâll call this futureSavings A
.
The ongoing payments are a little tricker (a future value series, see the reference below. Weâll call this one futureSavingsB
.
Here are those equations:
futureSavings = futureSavingsA + futureSavingsB
futureSavingsA = startingPot * (1+interestRate)^n
(this is just compound interest)
futureSavingsB = (annualIncome * savingsRate) * ((1+interestRate)^n - 1) / interestRate
(this is a future value series, see reference below)
Combine the two equations and rearrange
We take this, combine it with the expenses formula earlier, and rearrange to remove FutureValue
and CurrentExpenses
.
Equation 1) currentExpenses = futureSavings * SWR%
Equation 2) currentExpenses / withdrawalRate = [startingPot * (1+interestRate)^n] + [(annualIncome * savingsRate) * ((1+interestRate)^n - 1) / interestRate]
Combined Equations) ((1 - savingsRate) * annualIncome)) / withdrawalRate = [startingPot * (1+interestRate)^n] + [(annualIncome * savingsRate) * ((1+interestRate)^n - 1) / interestRate]
We do some fairly heavy rearranging, and then take the natural logarithm of either side (see reference below).
An equation to find ânâ (years to FI) based on savings rate
n = (ln((annualIncome * (interestRate * (-savingsRate) + interestRate + savingsRate * withdrawalRate)) / (withdrawalRate * (annualIncome * savingsRate + initialValue * interestRate)))) / (ln(interestRate + 1))
^^NOTE: this uses logarithms
And thatâs what you pop into Excel to generate the chart above .
References: