In this post, I’ll show how you and I can become **financially independent** and **retire young**.

The best thing about it? Everyone can follow the exact same strategy. It involves no magic, risky investments or lottery wins…

… but it involves hard work and discipline to succeed with it.

Before we get started, let’s agree about what **financial independence** is. To me, it means:

The state of having sufficient money to continue living your current lifestyle without having to work

The part about ‘*continue living your current lifestyle*‘ is crucial to understand. Financial independence (to me) does not mean being able to spend a million dollars in Las Vegas – if you have not done that prior to retirement of course.

## The only concept you need to know: Your savings rate

The concept of **financial independence** is actually extremely simple.

You can find a lot of amazingly complex literature on the subject, but it is really not necessary. If you want to understand the more advanced stuff, read the last part of this post.

If you want to retire young, you only need to know one simple concept: **Your savings rate**. This is it! Nothing more, nothing less! The savings rate says everything – it even tells you how soon you will be able to retire. Let me give you an example:

If your **savings rate is 75%**, you will be financially independent and ready to **retire in approximately 7 years** from now.

Sounds crazy? It is simple math. Let’s get started.

## The super simple math behind your savings rate

The key to understanding the savings rate, is to understand the few simple components of it:

Savings rate = Monthly savings / Monthly take-home income

It is pretty basic right? The higher your monthly savings as a share of your monthly take-home income, the higher the savings rate. **A higher savings rate means earlier retirement** – simple as that.

The savings rate can be computed weekly or yearly, but I like to keep track on a monthly basis as that is when I receive my salary.

Don’t believe that the savings rate is everything you need? Let me give you an example:

Bob is a carpenter and earns $35,000 per year. He saves up $3,500 per year (10% savings rate)

Michael is an investment banker and earns $350,000 per year. He saves up $35,000 per year (10% savings rate)

Who will be able to retire first? (Drum roll…) You guessed it, they will be able to retire at exactly the same time – and **with a 10% savings rate that will be in roughly 50 years from now**.

Wait a minute… 50 years from now? **That is not early retirement**!

Many people have been taught to save 10% of their income. This is good for anyone who want to retire at 60-something.

If you want to **reitre young and achieve financial freedom**, you have to be much more ambitious than that.

By now, you are probably wondering how I calculate the link between the savings rate and the years until retirement. It is slightly technical, and we will get there if you keep on reading.

## How to master your savings rate

You have now learned about the simple concept of the savings rate. There are two (equally simple) ways of mastering the savings rate:

**Earn more money****Spend less money**

… and ideally a combination of the two. I know it sounds ridiculously simple and as a concept it is, but in reality it can be hard.

If you have to choose one of the two ways? **Spending less money will always be more powerful than earning more money**. It will probably easier as well.

Let’s assume you are currently earning $1.000 and save $500 (50% savings rate). By earning $100 more, you will be able to save $100 more and get a savings rate of 54.5% ($600/$1100).

Yet, by spending $100 less, you will be able to save $100 more and get a savings rate of 60% ($600/$1000). This being said, a combination of earning more and spending less will always be best.

## Planning your financial freedom and early retirement

Are you interested in achieving financial freedom and early retirement? Great, let’s get started. I suggest three actions that you can make today:

### 1. Calculate your current savings rate

Calculate your own current savings rate for the past few months. You can calculate this in two different ways:

A: Monthly savings / Monthly take-home income

B: 1 – (Monthly expenses / Monthly take-home income)

The **monthly take-home income** is the money that lands in your bank account after taxes.

The **monthly expenses** include all money that leaves your bank account (mortgage payments, personal loans, student loans, housing, food, transportation, etc.).

The **monthly savings** include liquid money that you can freely put in a savings account or invest. It does not include locked pensions.

Take your current savings rate and use the graph in step 3 to see how many years you have until retirement.

### 2. Set a realistic savings rate target

The most important decision you will make is to set a realistic savings rate target. This is what will earn you financial freedom and early retirement.

The savings rate target will determine what kind of life you will be living. It will influence all your decisions going forward.

**My recommendation is to calculate your ‘basic necessity savings rate’ first.**

This savings rate is the bare minimum of what you need to survive. It should only include shelter/housing, food and healthcare expenses. For most people, even these expenses can easily be decreased depending on how frugal (or ‘extreme’) you want to live.

Once you have the ‘basic necessity savings rate’ you should use the graph in step 3. Here you can see how many years you have until retirement with that savings rate.

Now compare your **current savings rate** (from step 1) and your **basic necessity savings rate** (from step 2).

**The true answer to your realistic savings rate target probably lies somewhere between these.**

Your **target savings rate** should be closer to the ‘basic necessity savings rate’. For the very dedicated, frugal people, it is most likely lower.

You will constantly be balancing a trade-off. You can either save money and stop buying things or prolong the number of years you have to be a slave of your work.

Do you really need to live in the city center? Do you really need to drive a car instead of biking? Do you really need that Starbucks coffee instead of brewing coffee at home? Do you really need a Netflix subscription? Do you really need to eat at fancy restaurants instead of cooking at home?

Your answer to these questions might be yes. You just have to realize that if the answer is yes, you might also have to work for the next 50 years to sustain it.

What if I asked you whether you wanted to drop all the above, but retire in 5 years instead? What would the answer be? This is the exercise you now have to make and decide for yourself.

### 3. Estimate your years to retirement

The graph below is used to estimate your time to retirement at different savings rates. Try to take your savings rate target and see how many years you have to financial freedom.

Does it take too long and do you want to **become financially independent earlier**?

Well, then you know the two strategies you have at hand: you can either start spending more or saving less.

Figure out which one you choose and set a new savings rate target that you are comfortable with.

[Graph]**This is everything you need to do to start the journey** towards early retirement and financial freedom. You should follow this blog, for tips on how to increase savings and decrease spending.

Now, what I haven’t touched upon is investing money, eliminating debt (this should be a #1 priority for everyone!), making budgets and making them work, breaking social norms, dealing with reactions from friends and family, and many other good tips to improving your savings rate and living a simple, frugal life, but I’ll save that for later posts.

Okay, I promised all you math geeks a bit of background on the calculations used above, so here goes:

## The more advanced math behind the savings rate and early retirement

Listen up, geeks!

First, let’s start with the assumptions. I have kept them relatively conservative to avoid a massive outrage in the comments. I know that all of them can be discussed. In reality, you might be able to retire earlier or later than what the calculation shows.

**You will continue living the same life as you do today**– nothing more, nothing less**Once you retire, you will not have to work for a single cent ever again**– consider any paid work you do as an extra, but unnecessary bonus**The return on investments after inflation will be 5% annually**– looking at historical return rates, this is slightly below the average annual returns of the US stock market at roughly 6%

I actually use two methods to calculate my time to retirement. I call them the “safe” and “die poor” strategies. Both of the strategies have the savings rate at their core.

**I prefer the safe strategy and would always recommend it**.

The die poor strategy only comes in handy, if you are more than 40-50 years old.

The **safe strategy** is the most bulletproof and safe way to retirement.

## The advanced math behind the ‘safe strategy’ (my favorite strategy by far!)

Before we get started on the safe strategy, you should be aware of two more assumptions. These are what makes this strategy the best one for early retirement:

**Your net worth should never decline**once it has been built, thus you will only live off the returns on the investments.**Your withdrawal rate will be a maximum of 4% annually**of your net worth. This means that you will not withdraw more than 4% of your total net worth. I promise to make an in-depth post about this at some point – until then, trust me when I say that this is safe, although nothing is ever 100% safe. The actual term for this is the ‘safe withdrawal rate’

The beauty of these two assumptions is that you can continue to live forever and never run out of money. You will only withdraw what is safe and only spend your investment returns. You do not care about fluctuations in returns or the global economy (unless there is a structural change in returns over a long period of time). This is what I call real financial freedom.

I guess you want to **calculate your own time to retirement**? Let’s get started on this! We are going to use the following variables:

- Years to retirement in year 0 = Y
- Months to retirement in year 0 = M
- Existing savings in year 0 = C
- Total net worth in a given year = NW
- Monthly take-home income = MT
- Annual savings rate in years of take-home income = S
- Annual expense rate in years of take-home income = E = 1 – S
- Annual investment returns (after inflation) = AIR
- Monthly investment returns (after inflation) = MIR = (1 + AIR)^(1/12) – 1
- Safe withdrawal rate = SWR

Now, the first thing you want to do is:

### 1. Make an equation for how many months of take-home income your net worth (NW) makes up after a certain amount of months (M)

NW = (C/(MT*12) * ((1+MIR)^M) + S/12 * ((1+MIR)^(M+1)-(1+MIR))/MIR

The first part of the equation calculates the return on your existing savings, C (as a share of annual take-home income).

The second part of the equation calculates the return on the monthly contributions.

I suggest using months to calculate the above due to the interest/return accumulations.

Why do I use months? You most likely get salary monthly, and thus are able to generate returns from monthly contributions (savings).

If you use years, you have to decide on calculating returns of a year’s worth of savings at the beginning or end of the year.

Next step is to:

### 2. Make an equation for how large your net worth is compared to your spending

Relative net worth to spending (RNWS) = NW / E = NW / (1-S)

The reason for doing this is to know how many years we could potentially live (assuming no inflation would eat the savings or no returns would be made). Finally, you should:

### 3. Calculate how large a share of your spending that the safe withdrawal rate would give you:

SWR share of spending (SWRSS) = RNWS * SWR

The **SWRSS is important** because it shows whether your safe withdrawal rate would be able to cover all your expenses.

Now comes the fun part! The **SWRSS from above should be equal to 100%** at the exact year/month at which you can retire.

Next step is to calculate your **time to early retirement**. We can express it in one single equation:

### 4. Combine all of the above into one beautiful equation that will answer all your prayers:

We need to make sure that this equation equals 100%. This is because our safe withdrawal rate (SWR) taken from our total net worth (NW) in a given year, should be able to cover all our expenses.

100% = ((((C/(MT*12) * ((1+MIR)^M) + S/12 * ((1+MIR)^(M+1)-(1+MIR))/MIR)/(1-S)) * SWR

… and now it is fairly easy. We have all the numbers we need and only one unknown variable, which is the **number of months to retirement** (M). Let’s add the numbers to the equation:

- We assume no savings in year 0, thus C = 0
- We assume monthly take-home income of 5,000 USD (although since C = 0, it does not matter)
- The annual investment returns after inflation and taxes are assumed to be AIR = 5%
- … thus the monthly investment returns are ((1 + 5%)^(1/12) – 1) = MIR = 0.4074124%
- The safe withdrawal rate is SWR = 4% – once again, trust me that this is indeed a safe rate. I’ll explain it in a later post

Since we are assuming all the above numbers, we are only **left with figuring out one single input: our savings rate**. Once you have defined this, you will be able to calculate how soon your can retire.

This is why the **savings rate is the only concept you need to know** to retire early!

I will assume a **savings rate (S) of 50%** for now and insert the numbers into the equation:

100% = ((((C/(MT*12)) * ((1+MIR)^M) + S/12 * ((1+MIR)^(M+1)-(1+MIR))/MIR)/(1-S)) * SWR)

100% = ((((0/(5000*12)) * ((1+0.004074124)^M) + 0.5/12 * ((1+ 0.004074124)^(M+1)-(1+0.004074124))/0.004074124)/(1-0.5)) * 4%)

Now, this might seem a bit comprehensive to type in on a simple calculator.

I recommend you to use my tool on this website (coming soon!) or the **amazing WolframAlpha**. I have already used the latter and made you this link. You should look for the “Real solution”.

As you will see, the “real solution” lists **M = 195.846**.

Remember that this is **time to retirement in months**. To get number of years to retirement, we need to divide by 12: Y = 195.846 / 12 = 16.3 years.

In short: With a **savings rate of 50%**, you can retire in **16.3 years from now**.

Are you more ambitious than a 50% savings rate?

If you can **save 75% of your income**, you can can **retire in 7 years** from now.

If you can **save 90% of your income**, you can **retire in 2.6 years** from now.

Amazing, huh? And we haven’t even used any magic (yet).

## The advanced math behind the ‘die poor strategy’

I think you should always apply the **safe strategy** to be able to retire young and financially free. But you are curious – I understand it.

So, I want to present another way of calculating years to retirement: The die poor strategy.

This strategy will lead to a quicker retirement for people that are older (typically above 40-50 years old).

The basic premise is to earn as much (but only just as much!) money as you will be needing for the rest of your life – assuming you continue the same lifestyle. The variables used in the equation are as follows:

- Years to retirement (YR) = YR
- Years in retirement (YI) = (90 – your current age) – YR
- Annual investment returns after inflation (AIR) = AIR
- Monthly investment returns after inflation (MIR) = (1 + AIR)^(1/12) – 1
- Savings rate (S) = S
- Expense rate (E) = (1 – S)
- Current savings (C) = C

**Time to retirement** is the variable that you are interested in making as low as possible.

**Time in retirement** is self-explanatory and assumes that you will become 90 years old (higher than the average age today that is increasing).

**Investment returns and savings rate** is in percentage (e.g. 5% and 50% respectively).

**Current savings** given in a years’ worth of take-home income. For example if you have $10,000 in savings and earn $50,000 per year after tax, your current savings are 0.2 ($10,000/$50,000)).

### 1. The equation for calculating YR looks like this:

(YI*12) * (E/12) = C * (1+MIR)^(YR*12) + (S/12) * ((1+MIR)^(YR*12+1)-(1+MIR))/MIR

On the left side of the equation is the **money needed in retirement** at a given YR.

The right side is the amount of **money saved up for retirement** at a given YR.

You want to solve for the two sides to be equal to each other.

A short comment: We have multiplied all years with 12 to get to months and divided savings and expense rate with 12 to get the monthly savings and expenses.

We are doing this because most people get salaries on a monthly basis. Thus, you will start earning interest on monthly contributions straight away.

### 2. Simplifying the equation by substituting variables:

(90*12 – Your age * 12 – YR*12) * (1 – S/12) = C * (1+MIR)^(YR*12) + (S/12) * ((1+MIR)^(YR*12+1)-(1+MIR))/MIR

### 3. Applying the following assumptions to calculate years to retirement:

- Your age is 26
- Your savings rate (S) is 50%
- Annual investment returns (AIR) after tax are 5%, and monthly investment returns (MIR) after tax are (1 + 5%)^(1/12) – 1 = 0,41%
- You do not have any current savings
- In the years after retirement, you only invest in safe assets at low investment return rates – enough to offset inflation.

4. Inserting numbers into the equation:

(90*12-26*12-YR*12) * (1/12-0,5/12) = 0 * (1+0,41%)^(YR*12) + (0,5/12) * ((1+0,41%)^(YR*12+1)-(1+0,41%))/0,41%

Solving for YR gives years to retirement of:

YR = 22.6 years

Now, keep in mind that I am 26 years old and thus have a lot of years to save up to. If I had been 50 years old, YR would have been 15.9 years.

As a **general rule of thumb**, if you are young, you should apply the “safe strategy”, but if you are older you could consider the “die poor strategy”.

I hope that you are now even better educated in **why the savings rate is so damn important**. I hope that you have been inspired to become financially independent too.

*Any comments or reflections on how to retire young and achieve financial freedom? Or perhaps a few comments or corrections on the calculations above? Feel free to let me know in the comments.*

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## 6 comments

Hi Paul,

How do you make sure the investment return is 5% ? If I keep that into a savings account it won’t happen

I get 5% in my bank up to 50,000 DKK (8,000 USD), and then I am invested in stock indexes and peer-to-peer lending. So far, the 5% seems to be making sense.

Hi Carl,

Sorry for not being clear. Should MI not be MT?

Cheers.

Paul

Hi Paul,

You are absolutely right, thanks – I have corrected it now. Well spotted!

Onwards,

Carl

Hi Carl,

Are you sure the NW equation you give is right?

Regards,

Paul

Hi Paul,

I am relatively certain. What are your concerns?

Broken down, NW is in two parts:

1) (C/(MI*12) * ((1+MIR)^M)

2) S/12 * ((1+MIR)^(M+1)-(1+MIR))/MIR

The first gives the value of C (current net worth) as a share of yearly take-home income after M months.

The second gives the value of S (savings rate – savings’ share of take-home income, both yearly and monthly) after M months.

Then we need to find out when the value of 1) and 2) combined divided by (1 – S) * safe withdrawal rate = 1.

Does it makes sense? I have had another person question it as well, so I might be wrong!

Onwards,

Carl