# The Shockingly simple math behind early retirement

The Shockingly simple math behind early retirement is popularized by veteran blogger Mr. Money Mustache. You can check out his article here shockingly-simple-math-behind-early-retirement.

## WHAT IS SHOCKINGLY SIMPLE MATH?

Shockingly simple math tells you how many years it takes to achieve early retirement. It is purely based on one single factor.

`Your Savings percentage rate!`

Few assumptions remain constant:

1. 5 percent return adjusted for inflation.
2. 4 percent safe withdrawal rule.

#### 5 percent return adjusted for inflation:

The 5% return assumption made by MMM (Mr. Money Mustache) is pretty conservative. Even if you are going to invest in a low cost index fund the average rate of return is 8 percent or a bit more ( adjusted for inflation) on S&P 500 since 1900.

So automatically the years to retire corelated with the savings rate is also remain pretty conservative as you see in this post.

But this metric gives you an insight where you are standing on the journey of your early retirement, and also it shows you whether you need to amp up your savings rate or stay at the same pace.

#### 4 percent safe withdrawal rule:

Your annual spending and the size of your portfolio go hand in hand.

Assuming you have no source of other income and solely relied on your retirement portfolio.

But your spending has to remain constant in your retirement years. As you get old, you spend less compared to your young self. (Make sure you are covered by health insurance, I am sure you donâ€™t want to be generous in paying hospitals bills by breaking your retirement portfolio đź™‚

For example, If your annual spending is \$50,000 per year, by simply saving 25X of your annual spending you can achieve early retirement.

Formulae:

(Annual spending * 25)= Retirement portfolio

\$50,000 * 25 = \$1.25 million.

Also if your are withdrawing 4 % from \$1.25 million ( \$1.25 * 0.04= \$50K) , you can take out your annual spending amount \$50K without depleting your portfolio on your retirement years.

All the calculations are made on a assumption â€śZero Networthâ€ť.

If you have started investing in your 20â€™s regularly, then you are closer to your financial independence compared to the years you are about to see.

If your networth is below zero (Debt trap), get your finances straight and come out of the debt pit.

How many years does it take you to achieve 25X of your annual spending?

It entirely depends on the savings rate (i.e Investing) from your take home pay. Also your savings fund should be parked in instruments where it work towards your financial independence.

Your take home pay is divided into 2 categories:

1. Spending. (paying for services like grocery, rent)
2. Savings (Investing)

### Two ways to increase savings

You can reduce the years to retire by decreasing your spending. This will equip with a new skill â€średucing your spendingâ€ť, it will also decrease the size of your overall portfolio to achieve 25X.

Example:

Guy A spends \$ 50,000 per year, his portfolio should be (25 * \$50k) \$ 1.25 million in value.

Guy B spends \$ 40,000 per year, his portfolio value should be (25 * \$40K) \$ 1 million in value.

Reducing your spending on bills has a â€ť ceilingâ€ť. You canâ€™t keep chopping off your spending & live miserably for the sake of financial independence.

No matter how frugal we are , you canâ€™t live on \$2000 in a year unless you relocate to carton box.

The alternative way to increase your savings rate is increasing your income. unlike cutting the spending , there is no ceiling or upper limit to increase the income.

Your income is determined by how valuable your skills are. You can start doing freelancing, start a youtube channel to monetize, If you are into writing ;start to write on medium, turn your hobbies to profitable one.

Put in the work and follow the process, money wonâ€™t be a constraint.

### Does the Shockingly simple math principle hold:

The short answer is â€ť Yesâ€ť. The core principle of shockingly simple math hold.

Here is the chart

As the savings rate increases from 5% to 10% , the years to work till retirement shrink by 14 years (65 â€“ 51).

As you keep increasing the savings rate from 10% to 15%, the years to work till retirement again shrink by 9 years.

The rule of diminishing applies here, Hypothetically if your saving percentage increases 85% to 90%, years to retire will shrink by just a year.

But the whole point is as your savings rate increases , the years to work till retirement decreases.

Let us see some examples , how much is your portfolio value (25* annual spending) based on your savings percentage.

Assume a single middle-class household income is \$50,000 per year, Planning to save from new year with a networth of zero.

We here follow Mr. Money Mustacheâ€™s conservative return of 5% rate and 4 percent withdrawal rule.

Shockingly simple math @ 5% savings rate

With an income of \$50,000 per annum at a 5% savings rate , so the annual contribution would be \$2500 per year.

Portfolio Value

A family with an income of \$50,000 per year, annual spending of \$47,500 needs to target a portfolio of \$1.18 million dollars.

Though this approach takes the benefit of compounding due to long working years, but working is 65 years is pretty long unless you have a love for it.

The whole point is at a 5% savings rate, you need to work for good 65 years.

Shockingly simple math @ 10% savings rate

With an income of \$50,000 per annum at a 10% savings rate ,so the annual contribution would be \$5000 per year.

Portfolio Value

A household with a income of \$ 50,000 and an annual spending of \$45,000 needs to target a portfolio value of \$1.12 million.

There is also a decrease in 14 years when you increase your savings rate to 10% from 5%.

Also the annual spending is little bit less compared to the previous one, hence the size of the targeted portfolio shrinks.

Shockingly simple math @ 20% savings rate

With an income of \$50,000 per annum at a 20% savings rate , so the annual contribution would be \$10000 per year.

Portfolio target value

A household with an income of \$50,000 and an annual spending of \$40,000 needs to target a portfolio value of \$1million.

There is also a decrease in 15 years when you increase your savings rate to 20% from 10%.

Saving 20 % is bit challenging when you have kids and family, but its possible.

It takes 36 years to achieve your target portfolio when your savings rate are at 20%.

Shockingly simple math @ 30% savings rate

With an income of \$50,000 per annum at a 30% savings rate , so the annual contribution would be \$15000 / year.

Portfolio Target value

A household with an income of \$ 50,000 and an annual spending of \$35,000 needs to target a portfolio value of \$ 8,75,000.

8 years in decrease to achieve the target value, when you increase your savings rate contribution from 20 % to 30 %.

It also takes 28 years to achieve financial freedom at this savings rate.

Also my take home savings rate stands between 28% to 30% every month.

Shockingly simple math @ 50% savings rate

A household With an income of \$50,000 per annum at a 50% savings rate , so the annual contribution would be \$25000 per year.

Portfolio Target value

A household with an income of \$ 50,000 and an annual spending of \$25,000 needs to target a portfolio value of \$ 6,25,000.

It would 17 years to achieve the early retirement when you save at 50 % of your take home pay.

Also living on \$25K would be extremely difficult. Even though MMM (Mr. Money Mustache) is known for his frugality but his annual spending falls between \$28K â€“ \$30k per year.

Shockingly simple math @ 70% savings rate

With an income of \$50,000 per annum at a 70% savings rate , so the annual contribution would be \$35000 per year.

Portfolio target value

A household with an income of \$ 50,000 and an annual spending of \$15,000 needs to target a portfolio value of \$ 3,75,000 for early retirement.

It would take only 9 years to achieve financial independence at 70 % savings rate.

Only outliers can save at this rate!

Shockingly simple math @ 90% savings rate

With an income of \$50,000 per annum at a 90% savings rate , so the annual contribution would be \$45000 per year.

Portfolio target value

A household with an income of \$ 50,000 and an annual spending of \$5,000 needs to target a portfolio value of \$ 1,25,000 for early retirement.

It would take just 3 years to achieve financial independence when you save 90 percent of take home.

But living on \$5000 an entire year is highly impossible!

90 percent savings rate is just to illustrate how shockingly simple math works.

### Shockingly simple math chart at 8% return

Normally the average return of the S&P 500 is 8% on a long trend. You can see in the below chart how many years to take to achieve financial freedom at various savings rate with 8% rate of return.

There is a massive difference in the years to retire between 5% and 8% return.

By adhering to rule of 72 you can easily find out how many year does it takes for your money to double in your portfolio.

In the above case, 5% percent return is fixed. So your money in the portfolio would double in 14.5 years.

But in the real world, the returns in equity market is not fixed, Also we cannot predict the future returns of the market.

There are certain parameters apart from market returns, we can predict. They are:

• Income
• Expenses.

We will see in the next section how the shockingly simple math behind early retirement behaves when our income & expenses arises.

### Why Low spending high income is a cherry on the cake?

In the shockingly simple math match, the guy with low spending habits but earns high income beats the guy the with high income & high spending habits.

Ryan is a data scientists engineer brings in a cool \$150,000 per year home. He loves going to the beach,Â  walk in the sun, read books, Loves gardening, lives in a modest neighborhood.Â

Due to his less expensive habits & lifestyle, he saves about 60 percent of his annual income. Thatâ€™s a saving of \$90K.Â

Ryan spends \$60K / year. So he needs a portfolio of \$1.5 million.

Luke who lives in next street of Ryan also a product manager in tech giant makes a \$200000 per year. Luke loves cars & love to upgrade his car once in 3 years, takes his family to fine restaurants, both Luke & his wife loves to decorate their house with great interiors etc.

Due to Lukeâ€™s Lifestyle, he still manages to save 40 percent of his income. Thatâ€™s an annual saving of \$80K.

Luke spends \$120K/ Year. So he needs a portfolio of \$3 million to maintain his lifestyle during his retirement years.

#### Observations:Â

Luke needs 100% bigger portfolio than Ryan to retire.Â

Both Luke & Ryan are earning high income. But such a stark difference in the size of their retirement portfolio.

Why?Â

Its our behaviorsâ€™ & habits affects the spending , then our spending affect theÂ  savings rate , then our savings rate affect size of portfolio, then portfolio affects the shockingly simple math.

Do you see not only our investments get compounded, Even our behaviorâ€™s lead to compounding & chain reactions.

### Does the Shockingly simple math holds true as Income rises:

Most of the people who desire to achieve financial freedom and early retirement are mostly working class people.

Once we graduate and start getting a Job, year after year our pay increases unless its extreme situations like COVID-19.

In US, the average annual increment for an employee across corporates is 4%. Would you agree?

Assume Jack got job that pays him \$40,000 annually (post tax) and manage to save a decent 20% income which fetches him 5% rate of return.

As he performs well in the given task, his boss like to give him \$2000 increment year on year. Also Jack somehow manages to his expense same. His annual expense is \$32K.

To achieve financial freedom, Jack needs to have a target portfolio of \$800,000 (25X x \$32K = \$800K) to meet his expenses at 4% withdrawal rate.

Three Conditions remain constant are:

• \$2000 annual increment
• \$32K is annual expenses
• \$800K target portfolio

Please see the below image how years to achieve target varies as Jack pay rises.

Does the shockingly simple Math still hold true?

a) 5 percent rate of return is pretty conservative. On an average S&P 500 churns out 8 percent rate of return (adjusted for inflation).

When you get that kind of return , the number of years to work would decrease highly.

b) The sole purpose of financial independence is to live the life to fullest. Make the process of financial independence enjoyable.

Its a journey that matters, not only the destination.

c) Having a second source of income puts you on the fast lane to achieve early retirement.

It could be a part time job, digital marketing, Youtube channel etc.

Focus on learning , earning follows. Never works the other way around!

Finally , Thanks to Mr. Money Mustache for inspiring me to write this post.

Truly, It is Mr Money Mustache shockingly simple math behind early retirement!