Using the Rule of 72 is a simple method for getting an approximate idea of how long it takes for your money to double. So how can you use it in tracking your investments?

In a perfect world, investors would like to know, in advance, how long it will take to double their money in the stock market. Knowing exactly how long this will take is helpful in planning out portfolio diversification, and eventually achieving financial freedom.

But, how does one go about working out how long it might take to double the value of a portfolio?. Investors can easily become confused. Especially when it comes to accounts that receive annual interest. Then, they may reach for complex formulae, and spreadsheets. 

But, there’s a simpler, better way of calculating the period it will take to double one’s investment.

What is the Rule of 72?

The Rule of 72 refers to the mathematical concept that shows how long it will take an investment to double in value (in theory). It’s a simple formula that anyone can use to determine the approximate time when an investment will double at a given annualized rate of return.

However, the Rule of 72 only works for calculating compounding growth. Investors can use the Rule of 72 only for an account that earns compound interest, not simple interest. Additionally, the Rule of 72 works better with an interest rate ranging from 6% to 10%.

Besides being used to show exponential growth of a portfolio, the Rule of 72 is also used to show exponential decay. For example, the loss of purchasing power caused by inflation, or the drop in the population numbers.

Compound Growth vs. Simple Growth

Interest helps the portfolio growth, and allocating a certain amount of money to an account that earns interest is a smart move investors make. There are two types of growth, or interest — simple and compound, and these are crucial for using the Rule of 72.

Compound interest is added to the already existing interest, plus the principal amount of the loan or deposit.

This type of interest is calculated with the following formula:

A = P (1 + r) (n)

On the other hand, simple interest is added only to the original investment. The formula for simple interest is:

A = P (1 + Rt)

Compound interest is better, as it can reduce the time required to double the money in an account, and grows the investments exponentially.

In other words, compounding interest grows an investment more and more every year, since the interest gets calculated on progressively larger amounts. Whereas simple interest doesn’t compound on itself over time. 

Origins of the Rule of 72

While it may sound surprising, the Rule of 72, and the concept of interest aren’t new ideas. Even ancient civilizations, such as the Mesopotamian, Greek, and Roman, used them in transactions, and basic money management.

While it may not have been called the Rule of 72, it was always around. For example, lenders always wanted to know how to manage their investments, and the rate of return.

Who Came up With the Rule of 72?

The first person to ever take note of the Rule of 72 was Luca Pacioli. Pacioli was an Italian mathematician. He mentioned the Rule of 72 in his book Summa de Arithmetica, Geometria, Proportioni et Proportionalita (Summary of Arithmetic, Geometry, Proportions, and Proportionality), published in 1494.

Pacioli stated that people who wish to know how many years it will take to double their investment should always ‘keep the number 72 in mind.’

Pacioli never went deeper into defining or explaining the reasoning behind 72.

With that in mind, it could have happened that someone else invented the number to improve their calculation of the interest rate, and portfolio growth. Some even say that Albert Einstein was the one to invent the Rule of 72, but that was never confirmed.

Why Is It Called the Rule of 72?

There’s no specific reason this rule is called the Rule of 72. Still, it serves to replace the complex logarithmic calculation that most investors are having trouble dealing with. The exact formula for determining how many years it takes to double your money based on compounding interest, or growth, is:

ln(2) / ln(1 + (interest rate/100))

where “In” represents the natural log value.

Good mathematicians could use this formula to get accurate results by observing return rates, and natural logs. The actual number that’s derived from the formula is 69.3. However, since this number is not easy to work with, people usually replace it with 72, since it’s equally good in showing the approximate number of years necessary to double the investment.

Navexa’s portfolio tracker is even easier to use. Our portfolio tracker automatically calculates every aspect of portfolio performance for shares, cryptocurrency, cash accounts and more. 

How to Use the Formula?

To calculate how long it would take for the investment to double in value, one can use the following formula:

Years to double = 72 / expected rate of return

This method can also be used to calculate the expected rate of return.

Investors should divide 72 with the years to double to get the rate of return on their investment (expected rate of return = 72 / years to double).

This principle handles fractions, or portions of the year. Plus, the resulting rate of return includes compounding interest on the investment.

However, there are a few things to pay attention to:

• the interest rate should not be a decimal
• this formula should be applied to an investment that receives annual interest (compounding)
• the farther the interest rates are from 8%, the less accurate the results would be
• to calculate lower interest rates, one can drop the number to 71
• this formula is easily divisible, but not perfectly accurate

Rule of 72 — Variations

Since this principle provides an approximate result, sometimes investors use slight variations, like the Rule of 69, Rule of 70, or Rule of 73.

These numbers are used in the same way, and serve to calculate the years required for the investment to double in value.

Rule of 72 — Examples

Here’s a simple example of using the method to calculate how long it takes for the investment to double:

Let’s say an account earns 4% of annual interest.

dividing 72 by 4 would give the years it takes for the money to double – 18.

When used to show inflation, and other deprecating numbers, the formula is the same.

However, the final result will show the years it will take for the amount to be cut in half.

Both novice, and experienced investors could use the Rule of 72 to estimate the doubling time of their holdings. Since the Rule of 72 is easy to use, almost anyone can estimate how long it will take for a certain number to double in value.

Who Uses The Rule of 72?

Since this rule can be used outside of personal finance and investing, it’s also used by other experts who need to estimate how many years it will take for a value to double.

What Is the Rule of 72 Good For?

The Rule of 72 is a good method that can be applied to anything that grows (or decays) exponentially. For example:

• GDP
• Inflation
• Investment compounding interest rate
• Credit card debt
• House mortgage
• Car loan refinancing

How Does the Rule of 72 Work?

By using the Rule of 72, investors can get an approximation of the years it will take for their assets to double in value.

This makes the Rule of 72 one of the key personal finance formulae to understand for investingt. Plus, this rule gives a general idea of how many “doubles” an investor might get during their lifetime, or for a certain period.

Does It Show Accurate Results?

When it comes to the accuracy of this rule, the Rule of 72 provides approximate information about the desired time period.

This formula is a simplification of the more complex logarithmic equation. Investors who wish to get an accurate result would have to do the entire calculation, or use an electronic spreadsheet calculator.

Navexa’s smart portfolio tracker replaces the spreadsheet. It automatically shows portfolio growth, and helps investors get a clear insight into the years it takes to grow their wealth.

What Are the Things the Rule of 72 Can Determine?

As we previously mentioned, this rule is usually used to determine the rate of return on the investment. However, experts in various industries can also apply this principle to anything that is compounding, and this doesn’t necessarily involve money.

For example, a city’s population that grows/decreases by a certain percentage per year can also use the rule to check how long it would take for the population to double, or halve.

Limitations of This Principle

Besides not being completely accurate in showing data, this formula is also mainly applied to compounding interest accounts, not simple interest ones. What’s more, the Rule of 72 works better for lower interest rates, and is less precise as the interest rate increases.

Additionally, this calculation can’t be used to forecast how long it might take to get a double return with decentralized finance and cryptocurrency, due to high market volatility, and sudden changes in prices.

Speculating Future Returns With The Rule Of 72

When people invest, they often want to know how long it will take to double their money. However, predicting the exact number of years can be tricky. 

This is why the Rule of 72 exists. When used correctly, with an investment that involves compound interest,this formula is generally fairly accurate — provided, of course, the annualized rate of return remains consistent.

here are certain limitations investors should be aware of. This mathematical concept works only with accounts that receive compounding annual interest at lower rates. 

The higher the rates go, the less accurate the results will be. 

This principle doesn’t work with simple interest.

On the other hand, investors can slightly change the number, based on their annual interest rate. For example, some may use 69.3, or 73, depending on the percentage of their rate.

The Navexa portfolio tracker and reporting platform is a fast, accurate way to determine your annualized rate of return across shares, ETFs, cryptos, cash accounts and more. We handle all portfolio performance calculations behind the scenes so you can focus on better understanding your portfolio and returns. 

Part II in our series on self-directed investing.

Welcome to the second post in our series on self-directed investing.

Part one introduced the idea of taking ownership of your portfolio.

For those of us with the time, inclination and discipline, taking ownership of our portfolio makes more sense than trusting our financial future to fund managers who charge fees and who don’t always beat the market.

(Go here first if you haven’t read the post yet.)

In this second post, we’re going to discuss some of the important choices you need to make when creating and managing an investment portfolio.

These choices divide broadly into two major questions.

1. How will you approach building your investment portfolio?
   
2. Which assets will suit your approach?

There’s a lot to cover in this installment of the series, but we’re going to keep it simple to give you a broad overview (see the bottom of this page for a list of great in-depth articles we recommend for continued reading).

Before we get into the types of strategies and assets you might wish to consider, a quick word about investing in general.

No two investors are the same.

That might sound obvious, but it’s worth remembering that no single investment strategy can suit everyone.

In our experience, your best bet is to learn how different investors use various strategies to create and manage their portfolios…

Cherry pick the aspects that you identify with and that fit with your own goals…

And create a strategy that fits your own financial and personal situation.

This is better than trying to replicate what other people have done in the past.

Because they are not you. And now is not then.

There’s a vast number of factors to consider when forming your strategy and selecting investments for your portfolio.

Your financial goals, your obligations, your appetite for risk, the amount of time and energy you’re prepared to put into researching and monitoring your investments — these are just a few.

It’s important to be clear on where you’re at in your investment journey, your career and your life in order to build a strategy that will best serve your goals.

Your Game Plan: Buy And Hold, Value Investing And More

“You can’t adjust your portfolio based on the whims of the market, so you have to have a strategy in a position and stay true to that strategy and not pay attention to noise that could surround any particular investment.”

— John Paulson, Multi-Billionaire American Businessman

Like we said, our aim here is to give you a broad overview of the types of strategies you can deploy for your portfolio.

These portfolio management styles are by no means a comprehensive list of those at play in the markets today, but they do broadly represent the spectrum of approaches you’ll find among investors.

Buy & Hold Investing

‘Buy and hold’ investing is the ultimate slow and steady strategy.

This style of investing is exactly as it sounds: You buy investments with a view to holding them for a very long time — like decades.

This strategy hinges on the idea that, over the long term, stocks always go up and the returns are always good, if not spectacular.

You may have heard the phrase ‘time in the market is better than timing the market’.

Buy and hold investing is hands-off in that you make your decisions early, and then largely leave your portfolio to grow and generate income for a very long time.

Value Investing

A ‘value stock’ is a stock which an investor calculates to be trading at a lower price than it should be.

Value investors look to create portfolios full of assets that — according to their research and analysis — will rise over the medium term as the market price catches up to the true value of the business.

Warren Buffet is widely regarded as being one of the greatest at picking undervalued stocks and holding them long enough to generate substantial returns.

Value investing is more hands on than buy and hold.

But it is flexible, depending on what sorts of sectors and assets you dive into.

Growth Investing

Growth investing is more aggressive than the two strategies above.

The idea is to ‘buy high and sell higher’, using the momentum of a rising stock market to capture short and medium term gains from stocks riding high on a wave of optimism and economic growth.

Many tech companies can be classed as growth stocks.

Growth stocks tend to be smaller, faster growing businesses that are capturing market share.

Growth investing requires a higher tolerance for risk, and in most cases a more active approach to portfolio management (more frequent buying and selling).

Portfolio Theory

Portfolio theory is less about which types of stocks you invest in, and more about balancing the mix of assets you hold in a particular way.

The idea is to capture maximum upside from your portfolio while minimising the risk you take by being exposed to the market.

Key to this is diversification, which you no doubt have heard about before.

Diversification is a way to spread risk between distinctly different type of investments, like stocks, bonds, exchange traded funds and so forth.

Diversification is about creating a mix of investments that balance out gains and losses in the short term, and grows in value over the longer term. 

Choosing Investments
For Your Portfolio

“The secret is if you have a lot of stocks, some will do mediocre, some will do okay, and if one of two of ’em go up big time, you produce a fabulous result.”

— Peter Lynch, averaged 29.2% return for 23 years straight

There are many different types of assets you can invest in within your portfolio.

The sort you go for will depend on the strategy you pursue, which as we mentioned will depend on your goals, risk tolerance and so on.

We often talk about the types of assets and financial instruments in terms of a ‘risk ladder’.

At the bottom of the risk ladder is cash (or precious metals if you prefer, but we won’t discuss that here).

Cash

Cash in the bank is the simplest investment asset.

It guarantees your capital and gives you exact knowledge of your return (the interest rate).

It’s how most of us store our wealth by default.

The problem with cash, though, is that interest rates tend not to beat the inflation rate (meaning your cash’s value will diminish over time).

Bonds

Bonds are next up the risk ladder. A bond is a debt instrument.

You buy a bond from a government or business and they guarantee to pay you a fixed interest rate while you hold it.

Bonds are a common way for organizations to raise capital.

Interest rates on bonds tend to be better than what your cash will earn in the bank.

Stocks

Stocks essentially let you participate in a company’s activities.

You own a shares in a business. Those shares can rise, fall and pay income in the form of dividends.

Within stocks (or equities), there is another risk ladder, which spans from the bottom to the top of the business world.

Big, established companies that pay good dividends and have a record of climbing over the long term are known as blue-chip stocks, or sometimes income stocks.

Growth stocks are smaller businesses on an upward trajectory. They are riskier but can deliver bigger, faster returns.

Risker and more dynamic again are small-cap and penny stocks — small, unproven companies aiming to capture market share.

These stocks can rise and fall dramatically, meaning investors who hold their shares stand to gain and lose proportionally.

Mutual funds & ETFs

A mutual fund is an investment fund where many investors pool their capital and allow a professional fund manager to control it.

Mutual funds focus on certain sectors or types of investments.

Some mimic particular markets and all aim to deliver solid, reliable returns.

These funds do charge management fees, though, and require you to allow a third party to select the assets the fund invests in.

An ETF — or exchange traded fund — tracks an underlying index, like the ASX200, for example.

Owning shares in an ETF exposes your capital to a specific mix of assets.

Like stocks, ETFs vary greatly in risk depending on the sector or market they track.

Their popularity has exploded in the past few years.

The approach ETFs allow you to take — essentially buying an entire market or sector with low fees — appeals to some of the heaviest hitters in the financial world.

Buffett told CNBC he thinks using ETFs “makes the most sense practically all of the time”.

Mark Cuban, another billionaire rockstar of the investing world, also likes cheap index funds as a way for new investors to start building their wealth.

The growing FIRE (Financial Independence & Retiring Early) community is also quite fond of ETFs as a wealth building tool.

Again, this isn’t an exhaustive list of the types of assets available to Australian investors — we haven’t covered commodities and derivatives — but this gives you an idea of the basic options you have when creating a portfolio.

Selecting The Right Mix Of
Assets For Your Chosen Strategy

Choosing an investment strategy and a mix of assets for your portfolio requires, above all else, clarity.

You need clarity on what you want to achieve, what you’re prepared to risk, and how much time and energy you want to put into managing your portfolio.

Building a portfolio is a lot like buying a new car.

No car is going to suit two drivers the same.

Maybe you want a people mover that offers great fuel economy so you and your family can take a long, relaxing drive.

On the other hand, perhaps you want a high performance sports car that costs loads to fuel but which delivers extreme speed and handling.

Carefully consider your goals and what you’re prepared to do to hit those goals.

If you’ve never bought a stock before, go read about my experience buying my first shares and how a careful, deliberate approach has allowed me to more than triple my investment.

Recommended articles for further reading:

https://www.thebalance.com/top-investing-strategies-2466844

https://investormint.com/investing/types-of-stocks