the rule of 72

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pages: 150 words: 43,467

Maths on the Back of an Envelope: Clever Ways to (Roughly) Calculate Anything by Rob Eastaway

butterfly effect, Donald Trump, Mahatma Gandhi, Ronald Reagan, the rule of 72

For example, if your savings go up by 3.3% in one year, 3.1% the next, and 2.7% the year after that, you’re not far off the right number if you say that the total growth over three years will be 3.3 + 3.1 + 2.7 = 9.1% (and using Zequals, you can simplify it further: 3% + 3% + 3% = 9%). This is fine over short periods. But over longer periods there’s another handy rule of thumb: the Rule of 72. DOUBLE YOUR MONEY – THE RULE OF 72 If your bank pays you compound interest at 4%, how long will it be before you have doubled your money? This complex-sounding calculation can be answered with a deceptively simple rule. It’s known as the Rule of 72. Whatever the growth rate (be that 1.2%, 4%, 10% or even 30%), the time it will take for the quantity in question to double can be found by dividing it into 72. With an interest rate of 4%, your money in the bank will double in 72 ÷ 4 = 13 years.

So, for example, the first significant figure of 0.0063 is 6. It’s possible for a significant figure to be zero, including a number’s final digit. For example, if an athlete runs 100 metres in 10.28 seconds, that is 10.3 seconds to three significant figures, and 10 seconds to two significant figures. WHERE THE RULE OF 72 COMES FROM The ‘Rule of 72’ is found by working out how many iterations (years, for example) it takes for a number to double if it is growing at a fixed rate. To follow the derivation, you do need to be familiar with natural logarithms. Let’s call the annual interest rate R per cent. What we are looking for is the number of years, N, that it will take our starting pot of money, A, to double; i.e. after N years we will have an amount 2A: A × (1 + R)N = 2A Cancelling A on both sides: (1 + R)N = 2 Take logarithms of both sides: N.ln(1 + R)= ln 2 = 0.69 (= 69%) There is a rule of thumb familiar to mathematicians that if R is small then ln(1 + R) ≈ R (this is accurate to within 5% if R < 10%).

That is the figure that emerges from doing the algebra behind exponential growth (described in more detail here). But try dividing anything into 69.3 and you’ll end up with a mess. Whoever first worked out this rule quickly spotted that by nudging it up to 72 instead, there was a chance people would be able to work out the numbers on the back of an envelope – or even in their heads. So the Rule of 72 it is.2 Knowing how long it will take for numbers to double is handy, but there may be times when you want to know a different target. What about trebling your money, or increasing it tenfold? It turns out there is a rule of thumb for any target of growth that you choose. In each case, it uses a convenient number that is quite close to the accurate one.


pages: 505 words: 142,118

A Man for All Markets by Edward O. Thorp

3Com Palm IPO, Albert Einstein, asset allocation, Bear Stearns, beat the dealer, Bernie Madoff, Black Swan, Black-Scholes formula, Brownian motion, buy and hold, buy low sell high, caloric restriction, caloric restriction, carried interest, Chuck Templeton: OpenTable:, Claude Shannon: information theory, cognitive dissonance, collateralized debt obligation, Credit Default Swap, credit default swaps / collateralized debt obligations, diversification, Edward Thorp, Erdős number, Eugene Fama: efficient market hypothesis, financial innovation, Garrett Hardin, George Santayana, German hyperinflation, Henri Poincaré, high net worth, High speed trading, index arbitrage, index fund, interest rate swap, invisible hand, Jarndyce and Jarndyce, Jeff Bezos, John Bogle, John Meriwether, John Nash: game theory, Kenneth Arrow, Livingstone, I presume, Long Term Capital Management, Louis Bachelier, margin call, Mason jar, merger arbitrage, Murray Gell-Mann, Myron Scholes, NetJets, Norbert Wiener, passive investing, Paul Erdős, Paul Samuelson, Pluto: dwarf planet, Ponzi scheme, price anchoring, publish or perish, quantitative trading / quantitative finance, race to the bottom, random walk, Renaissance Technologies, RFID, Richard Feynman, risk-adjusted returns, Robert Shiller, Robert Shiller, rolodex, Sharpe ratio, short selling, Silicon Valley, Stanford marshmallow experiment, statistical arbitrage, stem cell, stocks for the long run, survivorship bias, tail risk, The Myth of the Rational Market, The Predators' Ball, the rule of 72, The Wisdom of Crowds, too big to fail, Tragedy of the Commons, Upton Sinclair, value at risk, Vanguard fund, Vilfredo Pareto, Works Progress Administration

To get quick approximate answers to compound interest problems like these, accountants have a handy trick called “the rule of 72.” It says: If money grows at a percentage R in each period then, with all gains reinvested, it will double in 72/R periods. Example: Your money grows at 8 percent per year. If you reinvest your gains, how long does it take to double? By the rule of 72, it takes 72 ÷ 8 = 9 years, since a period in this example is one year. Example: The net after-tax return from your market-neutral hedge fund averages 12 percent a year. You start with $1 million and reinvest your net profits. How much will you have in twenty-four years? By the rule of 72, your money doubles in about six years.

By the rule of 72, your money doubles in about six years. Then it doubles again in the next six years, and so forth, for 24 ÷ 6 = 4 doublings. So it multiplies by 2 × 2 × 2 × 2 = 16 and becomes $16 million. For more on the rule of 72, see appendix C. The rule of 72 can expose outrageous claims. My personal trainer went to a stock market seminar where the operators were pitching a method called “rolling stocks.” Selecting common stocks that would supposedly oscillate between two levels, they advised the investor to repeatedly buy low and sell high. The operators claimed the suckers could make 22 percent a month. Why would they bother to share their secret when, by putting $2,000 in a tax-deferred IRA and reinvesting their gains, they would have more than $46 trillion in ten years?

From: Ibbotson, Stocks, Bonds, Bills and Inflation, Yearbook, Morningstar, 2014. Siegal’s Stocks for the Long Run gives US returns from 1801. Dimson et al. give returns for sixteen countries and an analysis. The return series depends on the time period and on the specific index chosen. Appendix C * * * THE RULE OF 72 AND MORE The rule of 72 gives quick approximate answers to compound interest and compound growth problems. The rule tells us how many periods it takes for wealth to double with a specified rate of return, and is exact for a rate of 7.85 percent. For smaller rates, doubling is a little quicker than what the rule calculates; for greater rates, it takes a little longer.


pages: 543 words: 153,550

Model Thinker: What You Need to Know to Make Data Work for You by Scott E. Page

"Robert Solow", Airbnb, Albert Einstein, Alfred Russel Wallace, algorithmic trading, Alvin Roth, assortative mating, Bernie Madoff, bitcoin, Black Swan, blockchain, business cycle, Capital in the Twenty-First Century by Thomas Piketty, Checklist Manifesto, computer age, corporate governance, correlation does not imply causation, cuban missile crisis, deliberate practice, discrete time, distributed ledger, en.wikipedia.org, Estimating the Reproducibility of Psychological Science, Everything should be made as simple as possible, experimental economics, first-price auction, Flash crash, Geoffrey West, Santa Fe Institute, germ theory of disease, Gini coefficient, High speed trading, impulse control, income inequality, Isaac Newton, John von Neumann, Kenneth Rogoff, knowledge economy, knowledge worker, Long Term Capital Management, loss aversion, low skilled workers, Mark Zuckerberg, market design, meta-analysis, money market fund, Nash equilibrium, natural language processing, Network effects, p-value, Pareto efficiency, pattern recognition, Paul Erdős, Paul Samuelson, phenotype, pre–internet, prisoner's dilemma, race to the bottom, random walk, randomized controlled trial, Richard Feynman, Richard Thaler, school choice, sealed-bid auction, second-price auction, selection bias, six sigma, social graph, spectrum auction, statistical model, Stephen Hawking, Supply of New York City Cabdrivers, The Bell Curve by Richard Herrnstein and Charles Murray, The Great Moderation, The Rise and Fall of American Growth, the rule of 72, the scientific method, The Spirit Level, the strength of weak ties, The Wisdom of Crowds, Thomas Malthus, Thorstein Veblen, Tragedy of the Commons, urban sprawl, value at risk, web application, winner-take-all economy, zero-sum game

Using the equation, we can calculate that a $1,000 bond paying 5% annual interest increases in value by $50 in year one and by more than $100 in year twenty. To draw clean inferences, we assume a constant growth rate. Given that assumption, we can manipulate the exponential growth equation to derive the rule of 72. Rule of 72 If a variable grows by a percentage R (less than 15%) each period, then the following provides a good approximation: Periods to Double ≈ The rule of 72 quantifies the cumulative effect of higher growth rates. In 1966, Zimbabwe had a per capita GDP of $2,000, twice that of Botswana. Over the next thirty-six years, Zimbabwe experienced little growth. Botswana, meanwhile, averaged 6% growth, meaning that Botswana’s GDP doubled every twelve years.

But he ignored the potential for innovation—the focus of models later in this chapter. Innovation subverted the trend. The exponential growth model can be applied to the growth of species as well, and not just to rabbits. When you acquire a bacterial infection, tiny bacteria reproduce at incredible rates. Bacteria in human sinuses grow at around 4% a minute. By applying the rule of 72, we can calculate they double every twenty minutes. In a single day, each initial bacterial cell spawns over a billion offspring.2 Their growth stops when the physical constraint of your sinuses leaves them no room. Food constraints, predators, and lack of space all reduce growth. Some species, such as deer in suburban America or the hippos brought to Colombia by drug lord Pablo Escobar, encounter few constraints on growth and their population grows rapidly, though not at bacterial rates.3 A convex function with a positive slope increases at an increasing value.

In a less pluralistic society, the newspaper industry might have lobbied the government to stop Craigslist. Doing so would have slowed growth. Japanese Chinese Economic Dominance Linear model + rule of 72: From 1960 to 1970 Japan’s GDP grew at a 10% annual rate. A linear projection of continued 10% increases would result in a doubling of the Japanese economy every seven years (using the rule of 72). In 1970, Japanese per capita GDP was approximately $2,000 in current US dollars. Had that trend continued, by 2012 per capita GDP would have doubled six times, resulting in a per capita GDP of $128,000. Growth model: This model explains Japanese growth as due to investments in physical capital.


pages: 239 words: 60,065

Retire Before Mom and Dad by Rob Berger

Airbnb, Albert Einstein, asset allocation, buy and hold, car-free, cuban missile crisis, discovery of DNA, diversification, diversified portfolio, en.wikipedia.org, fixed income, hedonic treadmill, index fund, John Bogle, mortgage debt, passive investing, Ralph Waldo Emerson, the rule of 72, transaction costs, Vanguard fund, Yogi Berra, Zipcar

In that year, Pacioli published a book on mathematics called the Summa de arithmetica, geometria, proportioni et proportionalita (Summary of arithmetic, geometry, proportions, and proportionality.) In his work he describes what has become known as the Rule of 72. Here’s what he wrote: “In wanting to know of any capital, at a given yearly percentage, in how many years it will double adding the interest to the capital, keep as a rule [the number] 72 in mind, which you will always divide by the interest, and what results, in that many years it will be doubled. Example: When the interest is 6 percent per year, I say that one divides 72 by 6; 12 results, and in 12 years the capital will be doubled.”9 The Rule of 72 enables us to estimate how long it will take to double our money given a certain interest rate.

The result is an estimate of how many years it will take us to double our initial investment. For example, if we earn 7% annual interest on an investment, it will take us about 10 years to double our money (72/7 = 10.2 years). Earn 9% interest, and the time to double our money shrinks to about eight years (72/9 = 8). The Rule of 72 doesn’t account for additional investments. It assumes you invest one lump sum of money at the start. Still, it gives us a glimpse into the power of the Money Multiplier. The difference between 7% and 9% interest may not seem like much, yet at 9% we double our money in eight years rather than 10.

Like a tiny seed that grows into a mighty oak tree, small decisions we make today will supercharge our finances down the road. * * * 9 https://en.wikipedia.org/wiki/Rule_of_72#History 10 https://personal.vanguard.com/us/insights/saving-investing/model-portfolio-allocations 3 Key Takeaways The Rule of 72 offers an easy way to determine how long it will take you to double your money. It also gives us a glimpse into the importance of our investment returns. Small changes in investment returns, even “just” 0.3%, will, over the long run, have major effects on your wealth. Larger changes in investment returns, such as 1%, will have life-changing effects on your money.


Bulletproof Problem Solving by Charles Conn, Robert McLean

active transport: walking or cycling, Airbnb, Amazon Mechanical Turk, asset allocation, availability heuristic, Bayesian statistics, Black Swan, blockchain, business process, call centre, carbon footprint, cloud computing, correlation does not imply causation, Credit Default Swap, crowdsourcing, David Brooks, Donald Trump, Elon Musk, endowment effect, future of work, Garrett Hardin, Hyperloop, Innovator's Dilemma, inventory management, iterative process, loss aversion, meta-analysis, Nate Silver, nudge unit, Occam's razor, pattern recognition, pets.com, prediction markets, principal–agent problem, RAND corporation, randomized controlled trial, risk tolerance, Silicon Valley, smart contracts, stem cell, sunk-cost fallacy, the rule of 72, the scientific method, The Signal and the Noise by Nate Silver, time value of money, Tragedy of the Commons, transfer pricing, Vilfredo Pareto, walkable city, WikiLeaks

Compound growth is key to understanding how wealth builds, how enterprises scale quickly, and how some populations grow. Warren Buffett said: “My wealth has come from a combination of living in America, some lucky genes, and compound interest.”4 A really quick way to estimate compounding effects is to use the Rule of 72.5 The rule of 72 allows you to estimate how long it takes for an amount to double given its growth rate by dividing 72 by the rate of growth. So, if the growth rate is 5% an amount will double in about 14 years (72/5 = 14.4 years). If the growth rate is 15%, doubling occurs in four to five years. In a team meeting, Rob asked our research team what a $1000 investment in Amazon would be if you invested at the time of the initial stock offering in 1997.

Charles thought about it for about 90 seconds: He tried a low rate of compounding of 5%, where doubling occurs every 14 years, then a high rate of 50% where doubling occurs every 18 months, before settling on $100k. The actual answer is $83k based on a 36% compounding rate, doubling every 2 years. Pretty good with no facts, just the Rule of 72! Where do errors occur with the rule of 72? When there is a change in the growth rate, which of course is often the case over longer periods. This makes sense, as few things continue to compound forever (try the old trick of putting a grain of rice on the first square of a chessboard and double the number on each successive square).


pages: 368 words: 145,841

Financial Independence by John J. Vento

Affordable Care Act / Obamacare, Albert Einstein, asset allocation, diversification, diversified portfolio, estate planning, financial independence, fixed income, high net worth, Home mortgage interest deduction, money market fund, mortgage debt, mortgage tax deduction, oil shock, Own Your Own Home, passive income, risk tolerance, the rule of 72, time value of money, transaction costs, young professional, zero day

As a result, in year two, your original $100,000 increased its earning power by $250 with all other factors remaining the same. With each year that passes, the earning power increases: This is referred to as the power of compounding. You can truly appreciate this over time, because the outcome can be astonishing. The Rule of 72 Before I describe how to use the financial tables provided in the following pages, I would like to explain the Rule of 72, which unlocks the answer to how long it will take you to double your money. Of course, the answer to this depends on your interest rate (rate of return). Simply divide the assumed rate of return into 72. For example: • If your assumed rate of return is 10 percent, divide 10 into 72, which equals 7.2 years. • If your assumed rate of return is 5 percent, divide 5 into 72, which equals 14.4 years.

Tax System 12 Organizing and Retaining Your Records 15 Tax-Preparation Services 16 Accumulating Wealth through Tax Planning 18 ix ftoc.indd ix 26/02/13 11:17 AM x Contents Chapter 3 Chapter 4 Chapter 5 Chapter 6 ftoc.indd x Determining Your Financial Position 23 Figuring Your Financial Net Worth 24 Case Study: How One Couple Learned They Were Spending More Than They Earned 24 Making Sense of Cash Flow 35 Establishing Your Financial Goals 57 Finding Trusted Advisors 61 Managing Debt 67 Case Study: How Two Doctors Went Bankrupt in Only a Few Years—What Not to Do 67 Basic Principles for Managing Debt 71 Good Debt versus Bad Debt 73 Credit-Card Debt 74 Auto Loans 80 Student Loans 81 Home Mortgage Loans 82 Business and Investment Loans 86 Understanding Credit 87 Your Credit Report and Your Credit Score 89 Preventing Identity Theft 93 Analyzing Your Debt 94 Insuring Your Health and Life 99 Choosing a Health Insurance Plan 100 Long-Term Care Insurance 111 Disability Insurance 118 Life Insurance 122 Buying Insurance Policies 128 Protecting Your Property with Insurance 133 Case Study: How a Lack of Insurance Wiped Out One Woman’s Life Savings 134 Homeowner’s Insurance 136 Automobile Insurance 140 Umbrella Liability Insurance 144 Buying Insurance Policies 147 26/02/13 11:17 AM Contents Chapter 7 Chapter 8 Chapter 9 Paying for College 153 Case Study: How Not Saving for Your Child’s Education Can Ruin Your Finances—and Your Child’s 156 Conducting a “Needs Analysis” for Your Children’s College Educations 160 Strategies for Saving Money for College Education 162 Education Tax Deductions and Credits 179 Planning for Retirement 187 Case Study: Saving versus Not Saving for Retirement: The $1.7 Million Difference 187 Retirement Equation: Calculating Your Personal Point X 191 The High Cost of Waiting to Save for Retirement 193 What You Can Expect to Receive from Social Security 196 Qualified Retirement Plans 198 The Difference between Traditional IRAs and Roth IRAs 203 Fixed and Variable Annuities 209 Retirement Funding: “Needs Analysis” 212 Managing Your Investments 221 Analyzing Your Risk Tolerance 222 Stocks, Bonds, Mutual Funds, and Exchange-Traded Funds 226 Diversification and Modern Portfolio Theory 234 Asset Allocation and Rebalancing 237 Dollar-Cost Averaging 243 Inflation and Taxes: The Biggest Drains on Investment Return 245 Medicare Surtax on Net Investment Income 246 Chapter 10 Preserving Your Estate ftoc.indd xi xi 251 The Federal Gift and Estate Tax System 252 Legal Documents to Consider for Estate Planning 252 The Probate and Administration Process and Why You May Want to Avoid It 257 Using a Planned Gifting Strategy 261 Ownership of Property and How It Is Transferred 262 Reasons for Creating a Trust 265 Benefit from a Family Limited Partnership 277 Estate Tax Planning and Life Insurance 278 26/02/13 11:17 AM xii ftoc.indd xii Contents Chapter 11 The Time Value of Money 285 The Rule of 72 286 Appendix A: Selecting a Trusted Advisor 301 Appendix B: 101 Ways to Save $20 or More per Week 311 Appendix C: Basic Concepts and Definitions of Various Types of Taxes 321 About the Author 341 Index 343 26/02/13 11:17 AM Preface Living the American Dream M y first clients were quintessential examples of successful American Dreamers.

This example verifies that time is money and that one of your most valuable financial assets is time. By getting off to an early start with your retirement savings program, you can take advantage of the power of compounding. Your annual savings have the potential of earning a rate of return, and so does your reinvested earnings. Look at the Rule of 72 in Exhibit 11.1 to see just how powerful compounding can be. This is the secret to financial independence: by letting your money work for you, eventually, you will no longer have to work to maintain your desired standard of living. If you have been finding it difficult to save money on a regular basis, implement the following savings strategies that will take money directly from your paycheck on a pre-tax basis.


pages: 261 words: 70,584

Retirementology: Rethinking the American Dream in a New Economy by Gregory Brandon Salsbury

Albert Einstein, asset allocation, Bear Stearns, buy and hold, carried interest, Cass Sunstein, credit crunch, Daniel Kahneman / Amos Tversky, diversification, estate planning, financial independence, fixed income, full employment, hindsight bias, housing crisis, loss aversion, market bubble, market clearing, mass affluent, Maui Hawaii, mental accounting, mortgage debt, mortgage tax deduction, National Debt Clock, negative equity, new economy, RFID, Richard Thaler, risk tolerance, Robert Shiller, Robert Shiller, side project, Silicon Valley, Steve Jobs, the rule of 72, Yogi Berra

In the world of finance, many professionals utilize a mathematical formula called the Rule of 72, and it provides a thumbnail estimate of how long it may take an investor’s portfolio to double in value. The Rule of 72 simply divides 72 by the assumed rate of return to get a rough estimate of how many years it will take for the initial investment to double. For example, if we assume a rate of return of 7.2%, your money will double every 10 years. (Using this rule, at a 10% rate of return, your money would double in 7.2 years.) Simple as that. However, when you apply the reality of taxation, the formula can change dramatically. The Rule of 72 becomes a concept I call 72/33/50; assuming a 33% tax rate, it takes 50% longer to double your money.


pages: 389 words: 81,596

Quit Like a Millionaire: No Gimmicks, Luck, or Trust Fund Required by Kristy Shen, Bryce Leung

"side hustle", Affordable Care Act / Obamacare, Airbnb, asset allocation, barriers to entry, buy low sell high, call centre, car-free, Columbine, cuban missile crisis, Deng Xiaoping, Elon Musk, fear of failure, financial independence, fixed income, follow your passion, hedonic treadmill, income inequality, index fund, John Bogle, longitudinal study, low cost airline, Mark Zuckerberg, mortgage debt, obamacare, offshore financial centre, passive income, Ponzi scheme, risk tolerance, risk/return, Silicon Valley, single-payer health, Snapchat, Steve Jobs, supply-chain management, the rule of 72, working poor, Y2K, Zipcar

If I invest $1,000 with a return of 6 percent a year, it’ll compound into $2,000 in 12 years without my investing another cent. That balance goes up over time, because the money I make makes more money, which in turn makes even more money. When you’re an investor, the Rule of 72 is your friend. It helps your money grow. But if you have debt, the Rule of 72 is your enemy. It works against you to take what little money you have. Credit cards typically have interest rates around 20 percent, so if I borrow $1,000 to buy a flat-screen TV, it would take only 72 / 20 = 3.6 years for my debt to double. Another 3.6 years and the debt quadruples.

Since consumer debt has the highest interest rate, you want to slay this bad boy first. Consumer debt should be treated as what it is: a financial emergency that you have to take care of now. Here are a few things you can do to sharpen your stake. 1. Cut expenses to the bone, even if it hurts. Consumer debt has the highest interest rate of all and, as per the Rule of 72, doubles faster than any other type of debt. You need to treat this as a crisis. There is absolutely no point in investing or even saving much cash if you’re carrying debt with a 10–20 percent interest rate. Paying it off should be your number one financial priority. If you need to get a side gig or a roommate, or learn to say no to dinners out, do it. 2.


pages: 335 words: 94,657

The Bogleheads' Guide to Investing by Taylor Larimore, Michael Leboeuf, Mel Lindauer

asset allocation, buy and hold, buy low sell high, corporate governance, correlation coefficient, Daniel Kahneman / Amos Tversky, diversification, diversified portfolio, Donald Trump, endowment effect, estate planning, financial independence, financial innovation, high net worth, index fund, John Bogle, late fees, Long Term Capital Management, loss aversion, Louis Bachelier, margin call, market bubble, mental accounting, money market fund, passive investing, Paul Samuelson, random walk, risk tolerance, risk/return, Sharpe ratio, statistical model, stocks for the long run, survivorship bias, the rule of 72, transaction costs, Vanguard fund, yield curve, zero-sum game

THE MAGIC IS IN THE COMPOUNDING Most people earning $25,000 a year believe that their only shot at becoming a millionaire is to win the lottery. The truth is that the odds of anyone winning a big lottery are less than the odds of being struck twice by lightning in a lifetime. However, the power of compound interest and the accompanying Rule of 72 illustrate how anyone can slowly transform small change into large fortunes over time. The Rule of 72 is very simple: To determine how many years it will take an investment to double in value, simply divide 72 by the annual rate of return. For example, an investment that returns 8 percent doubles every 9 years (72/8 = 9). Similarly, an investment that returns 9 percent doubles every 8 years and one that returns 12 percent doubles every 6 years.

We are too soon old and too late smart. 0 Youth is too precious to be wasted on the young. If you are a young person, we strongly encourage you use the leverage of your youth to make the power of compounding work for you. And if you are no longer young, it's even more important. Use the time you have to make the Rule of 72 work for you. THIS ABOVE ALL: SAVING IS THE KEY TO WEALTH As you will soon learn, the Boglehead approach to investing is easy to understand and easy to do. It's so simple that you can teach it to your children, and we urge you to do so. For most people the most difficult part of the process is acquiring the habit of saving.


pages: 357 words: 91,331

I Will Teach You To Be Rich by Sethi, Ramit

Albert Einstein, asset allocation, buy and hold, buy low sell high, diversification, diversified portfolio, index fund, John Bogle, late fees, money market fund, mortgage debt, mortgage tax deduction, prediction markets, random walk, risk tolerance, Robert Shiller, Robert Shiller, shareholder value, Silicon Valley, survivorship bias, the rule of 72, Vanguard fund

You’ll need to invest the money to start making good returns. The easiest investment is a lifecycle fund. You can just buy it, set up automatic monthly contributions, and forget about it. (If you really want more control, you can pick individual index funds instead of lifecycle funds, which I’ll discuss on page 188.) The Rule of 72 * * * The Rule of 72 is a fast trick you can do to figure out how long it will take to double your money. Here’s how it works: Divide the number 72 by the return rate you’re getting, and you’ll have the number of years you must invest in order to double your money. (For the math geeks among us, here’s the equation: 72 ÷ return rate = number of years.)


pages: 117 words: 31,221

Fred Schwed's Where Are the Customers' Yachts?: A Modern-Day Interpretation of an Investment Classic by Leo Gough

Albert Einstein, banking crisis, Bernie Madoff, corporate governance, discounted cash flows, disinformation, diversification, fixed income, index fund, John Bogle, Long Term Capital Management, Northern Rock, passive investing, Ralph Waldo Emerson, random walk, short selling, South Sea Bubble, The Nature of the Firm, the rule of 72, The Wealth of Nations by Adam Smith, transaction costs, young professional

The situation is even beter if you can get a real rate of return of 7%, which is about the highest return you can realistically aim at from the stock market without taking excessive risk: after 5 years, the sum will have grown to £140, after 10 years to £197, after 20 years to £387 and after 25 years to £543. A useful way to estimate how long it will take an investment to double at a given rate of interest is ‘the rule of 72’. Simply divide the annual interest rate into 72, and you will get the approximate length of time it will take to double. For example, how long does it take for £100 to double at a return of 5%? 72/5 = 14.4, so it will take about 14.4 years. Since a small increase in the rate of return will make a huge difference to the growth of your investment over the long term, it is important to minimise investment charges because they can substantially reduce your overall return in later years.


pages: 621 words: 123,678

Financial Freedom: A Proven Path to All the Money You Will Ever Need by Grant Sabatier

"side hustle", 8-hour work day, Airbnb, anti-work, asset allocation, bitcoin, buy and hold, cryptocurrency, diversified portfolio, Donald Trump, financial independence, fixed income, follow your passion, full employment, Home mortgage interest deduction, index fund, loss aversion, Lyft, money market fund, mortgage debt, mortgage tax deduction, passive income, remote working, ride hailing / ride sharing, risk tolerance, Skype, stocks for the long run, stocks for the long term, TaskRabbit, the rule of 72, time value of money, uber lyft, Vanguard fund

That $60,000 vintage car is actually costing you $486,989 in the future. So you are actually trading 2,000 hours of your life AND over $400,000 in growth potential. I would rather have the money in the future, but your choice is up to you. Double your money with the Rule of 72. A simple way to estimate how much something will be worth at 7 percent compounding is to use the rule of 72, in which you divide 72 by your expected compounding rate (7 percent) to determine how many years it would take for your money to double. At 7 percent compounding, 72/7 percent = 10.2 years, so at that compounding rate, your money will double every ten years.


pages: 518 words: 128,324

Destined for War: America, China, and Thucydides's Trap by Graham Allison

9 dash line, anti-communist, Berlin Wall, borderless world, Bretton Woods, British Empire, capital controls, Carmen Reinhart, conceptual framework, cuban missile crisis, currency manipulation / currency intervention, Deng Xiaoping, disruptive innovation, Donald Trump, facts on the ground, Flash crash, Francis Fukuyama: the end of history, game design, George Santayana, Haber-Bosch Process, industrial robot, Internet of things, Kenneth Rogoff, liberal world order, long peace, Mark Zuckerberg, megacity, Mikhail Gorbachev, Monroe Doctrine, mutually assured destruction, Nelson Mandela, one-China policy, Paul Samuelson, Peace of Westphalia, purchasing power parity, RAND corporation, Ronald Reagan, Scramble for Africa, selection bias, Silicon Valley, Silicon Valley startup, South China Sea, special economic zone, spice trade, the rule of 72, The Wealth of Nations by Adam Smith, too big to fail, trade route, UNCLOS, Washington Consensus, zero-sum game

In 1980, China’s trade with the outside world amounted to less than $40 billion; by 2015, it had increased one hundredfold, to $4 trillion.4 For every two-year period since 2008, the increment of growth in China’s GDP has been larger than the entire economy of India.5 Even at its lower growth rate in 2015, China’s economy created a Greece every sixteen weeks and an Israel every twenty-five weeks. During its own remarkable progress between 1860 and 1913, when the United States shocked European capitals by surpassing Great Britain to become the world’s largest economy, America’s annual growth averaged 4 percent.6 Since 1980, China’s economy has grown at 10 percent a year. According to the Rule of 72—divide 72 by the annual growth rate to determine when an economy or investment will double—the Chinese economy has doubled every seven years. To appreciate how remarkable this is, we need a longer timeline. In the eighteenth century, Britain gave birth to the Industrial Revolution, creating what we now know as the modern world.

This was reflected in the 2010 US Nuclear Posture Review’s assertion that the US would not take any action that could negatively affect “the stability of our nuclear relationships with Russia or China.” [back] 63. Since 1988, China has spent an average of 2.01 percent of GDP on its military, while the US has spent an average of 3.9 percent. See World Bank, “Military Expenditure (% of GDP),” http://data.worldbank.org/indicator/MS.MIL.XPND.GD.ZS. [back] 64. Recall the Rule of 72: divide 72 by the annual growth rate to determine how long it will take to double. [back] 65. International Institute for Strategic Studies, The Military Balance 2016 (New York: Routledge, 2016), 19. [back] 66. Eric Heginbotham et al., The U.S.-China Military Scorecard: Forces, Geography, and the Evolving Balance of Power, 1996–2017 (Santa Monica, CA: RAND Corporation, 2015), xxxi, xxix.


The Intelligent Asset Allocator: How to Build Your Portfolio to Maximize Returns and Minimize Risk by William J. Bernstein

asset allocation, backtesting, buy and hold, capital asset pricing model, commoditize, computer age, correlation coefficient, diversification, diversified portfolio, Eugene Fama: efficient market hypothesis, fixed income, index arbitrage, index fund, intangible asset, John Bogle, Long Term Capital Management, p-value, passive investing, prediction markets, random walk, Richard Thaler, risk free rate, risk tolerance, risk-adjusted returns, risk/return, South Sea Bubble, stocks for the long run, survivorship bias, the rule of 72, the scientific method, time value of money, transaction costs, Vanguard fund, Yogi Berra, zero-coupon bond

Your inflation-adjusted portfolio expected return can be calculated as follows: 1. 25% of your portfolio in small stocks: .25 ⫻ 6% ⫽ 1.5% 2. 25% of your portfolio in large stocks: .25 ⫻ 4% ⫽ 1.0% 3. 50% of your portfolio in bonds: .5 ⫻ 3% ⫽ 1.5% Thus, the real long-term expected return of your portfolio is: 1.5% ⫹ 1% ⫹ 1.5% ⫽ 4% This means that you will about double the real value of your portfolio every 18 years. (This is easily calculated from “the rule of 72,” which says that the return rate multiplied by the time it takes to double your assets will equal 72. In other words, at 6% return your capital will double every 12 years.) Take another break. Don’t look at this book for at least a few more days. In the next chapter we shall explore the strange and wondrous behavior of portfolios.


pages: 670 words: 194,502

The Intelligent Investor (Collins Business Essentials) by Benjamin Graham, Jason Zweig

3Com Palm IPO, accounting loophole / creative accounting, air freight, Andrei Shleifer, asset allocation, business cycle, buy and hold, buy low sell high, capital asset pricing model, corporate governance, corporate raider, Daniel Kahneman / Amos Tversky, diversified portfolio, dogs of the Dow, Eugene Fama: efficient market hypothesis, Everybody Ought to Be Rich, George Santayana, hiring and firing, index fund, intangible asset, Isaac Newton, John Bogle, Long Term Capital Management, market bubble, merger arbitrage, money market fund, new economy, passive investing, price stability, Ralph Waldo Emerson, Richard Thaler, risk tolerance, Robert Shiller, Robert Shiller, Ronald Reagan, shareholder value, sharing economy, short selling, Silicon Valley, South Sea Bubble, Steve Jobs, stocks for the long run, survivorship bias, the market place, the rule of 72, transaction costs, tulip mania, VA Linux, Vanguard fund, Y2K, Yogi Berra

As of year-end 2002, the payout ratio stood at 34.1% for the S & P 500-stock index and, as recently as April 2000, it hit an all-time low of just 25.3%. (See www.barra.com/ research/fundamentals.asp.) We discuss dividend policy more thoroughly in the commentary on Chapter 19. * Why is this? By “the rule of 72,” at 10% interest a given amount of money doubles in just over seven years, while at 7% it doubles in just over 10 years. When interest rates are high, the amount of money you need to set aside today to reach a given value in the future is lower—since those high interest rates will enable it to grow at a more rapid rate.

* Today’s defensive investor should probably insist on at least 10 years of continuous dividend payments (which would eliminate from consideration only one member of the Dow Jones Industrial Average—Microsoft—and would still leave at least 317 stocks to choose from among the S & P 500 index). Even insisting on 20 years of uninterrupted dividend payments would not be overly restrictive; according to Morgan Stanley, 255 companies in the S & P 500 met that standard as of year-end 2002. † The “Rule of 72” is a handy mental tool. To estimate the length of time an amount of money takes to double, simply divide its assumed growth rate into 72. At 6%, for instance, money will double in 12 years (72 divided by 6 = 12). At the 7.1% rate cited by Graham, a growth stock will double its earnings in just over 10 years (72/7.1 = 10.1 years)


pages: 332 words: 81,289

Smarter Investing by Tim Hale

Albert Einstein, asset allocation, buy and hold, buy low sell high, capital asset pricing model, collapse of Lehman Brothers, corporate governance, credit crunch, Daniel Kahneman / Amos Tversky, diversification, diversified portfolio, Donald Trump, equity premium, Eugene Fama: efficient market hypothesis, eurozone crisis, fiat currency, financial independence, financial innovation, fixed income, full employment, implied volatility, index fund, information asymmetry, Isaac Newton, John Bogle, John Meriwether, Long Term Capital Management, Northern Rock, passive investing, Ponzi scheme, purchasing power parity, quantitative easing, random walk, risk free rate, risk tolerance, risk-adjusted returns, risk/return, Robert Shiller, Robert Shiller, South Sea Bubble, technology bubble, the rule of 72, time value of money, transaction costs, Vanguard fund, women in the workforce, zero-sum game

The cautious long-term investor Imagine that you are an investor that finds the whole concept of investment worrying and the loss of capital scares you. As a long-term investor of this ilk, there is one thing that you must protect against and that is inflation. Even at what seem relatively low levels of inflation, your spending power in retirement could be significantly eroded. Tip: The Rule of 72 is a useful one: divide 72 by the rate of inflation to see how quickly the price of goods will double. For example, with inflation of 3% the price of goods will double in 24 years (72/3 = 24). That is likely to be a risk that you simply cannot afford to take. Many very cautious investors simply put their cash on deposit.


pages: 416 words: 118,592

A Random Walk Down Wall Street: The Time-Tested Strategy for Successful Investing by Burton G. Malkiel

accounting loophole / creative accounting, Albert Einstein, asset allocation, asset-backed security, backtesting, Bear Stearns, beat the dealer, Bernie Madoff, BRICs, butter production in bangladesh, buy and hold, capital asset pricing model, compound rate of return, correlation coefficient, Credit Default Swap, Daniel Kahneman / Amos Tversky, diversification, diversified portfolio, dogs of the Dow, Edward Thorp, Elliott wave, Eugene Fama: efficient market hypothesis, experimental subject, feminist movement, financial innovation, fixed income, framing effect, hindsight bias, Home mortgage interest deduction, index fund, invisible hand, Isaac Newton, John Bogle, Long Term Capital Management, loss aversion, margin call, market bubble, money market fund, mortgage tax deduction, new economy, Own Your Own Home, passive investing, Paul Samuelson, pets.com, Ponzi scheme, price stability, profit maximization, publish or perish, purchasing power parity, RAND corporation, random walk, Richard Thaler, risk free rate, risk tolerance, risk-adjusted returns, risk/return, Robert Shiller, Robert Shiller, short selling, Silicon Valley, South Sea Bubble, stocks for the long run, survivorship bias, The Myth of the Rational Market, the rule of 72, The Wisdom of Crowds, transaction costs, Vanguard fund, zero-coupon bond

Next year, you also earn 10 percent on the $110 you start with, so you have $121 at the end of year two. Thus, the total return over the two-year period is 21 percent. The reason it works is that the interest you earn from your original investment also earns interest. Carrying it out in year three, you have $133.10. Compounding is powerful indeed. A useful rule, called “the rule of 72,” gives you a shortcut way to find out how long it will take to double your money. Take the interest rate you earn and divide it into the number 72, and you get the number of years it will take to double your money. For example, if the interest rate is 15 percent, it takes a bit less than five years for your money to double (72 divided by 15 = 4.8 years).


pages: 407 words: 116,726

Infinite Powers: How Calculus Reveals the Secrets of the Universe by Steven Strogatz

Albert Einstein, Asperger Syndrome, Astronomia nova, Bernie Sanders, clockwork universe, complexity theory, cosmological principle, Dava Sobel, double helix, Edmond Halley, Eratosthenes, four colour theorem, fudge factor, Henri Poincaré, invention of the telescope, Isaac Newton, Islamic Golden Age, Johannes Kepler, John Harrison: Longitude, Khan Academy, Laplace demon, lone genius, music of the spheres, pattern recognition, Paul Erdős, Pierre-Simon Laplace, precision agriculture, retrograde motion, Richard Feynman, Socratic dialogue, Solar eclipse in 1919, Steve Jobs, the rule of 72, the scientific method

You should get 90. As before, logs and exponentials undo each other’s actions like a stapler and a staple remover. Recondite as all this may sound, the natural logarithm is extremely practical, though often inconspicuously. For one thing, it underlies a rule of thumb known to investors and bankers as the rule of 72. To estimate how long it will take to double your money at a given annual rate of return, divide 72 by the rate of return. Thus, money growing at a 6 percent annual rate doubles after about 72/6 = 12 years. This rule of thumb follows from the properties of the natural logarithm and exponential growth and works well if the interest rate is low enough.


pages: 407 words: 114,478

The Four Pillars of Investing: Lessons for Building a Winning Portfolio by William J. Bernstein

asset allocation, Bretton Woods, British Empire, business cycle, butter production in bangladesh, buy and hold, buy low sell high, carried interest, corporate governance, cuban missile crisis, Daniel Kahneman / Amos Tversky, Dava Sobel, diversification, diversified portfolio, Edmond Halley, equity premium, estate planning, Eugene Fama: efficient market hypothesis, financial independence, financial innovation, fixed income, George Santayana, German hyperinflation, high net worth, hindsight bias, Hyman Minsky, index fund, invention of the telegraph, Isaac Newton, John Bogle, John Harrison: Longitude, Long Term Capital Management, loss aversion, market bubble, mental accounting, money market fund, mortgage debt, new economy, pattern recognition, Paul Samuelson, Performance of Mutual Funds in the Period, quantitative easing, railway mania, random walk, Richard Thaler, risk tolerance, risk/return, Robert Shiller, Robert Shiller, Savings and loan crisis, South Sea Bubble, stocks for the long run, stocks for the long term, survivorship bias, The inhabitant of London could order by telephone, sipping his morning tea in bed, the various products of the whole earth, the rule of 72, transaction costs, Vanguard fund, yield curve, zero-sum game

This means the market expected these companies to eventually increase their earnings relative to the size of the market to three or four times their current proportion. This is a tricky concept. Let us assume that the stock market grows its earnings at 5% per year. This means that over a 14-year period, it will approximately double its earnings. (This is according to the “Rule of 72,” which states that the earnings rate times the doubling time equals 72. In the above example, 72 divided by 5% is approximately 14. Or, alternatively, at a 12% growth rate, it takes only six years to double earnings.) If a glamorous growth company is selling at four times the P/E ratio of the rest of the market—say, 80 times earnings versus 20 times earnings—then the market is saying that during this same 14-year period, its earnings will grow by a factor of eight (4 × 2 = 8).


pages: 482 words: 121,672

A Random Walk Down Wall Street: The Time-Tested Strategy for Successful Investing (Eleventh Edition) by Burton G. Malkiel

accounting loophole / creative accounting, Albert Einstein, asset allocation, asset-backed security, beat the dealer, Bernie Madoff, bitcoin, butter production in bangladesh, buttonwood tree, buy and hold, capital asset pricing model, compound rate of return, correlation coefficient, Credit Default Swap, Daniel Kahneman / Amos Tversky, Detroit bankruptcy, diversification, diversified portfolio, dogs of the Dow, Edward Thorp, Elliott wave, Eugene Fama: efficient market hypothesis, experimental subject, feminist movement, financial innovation, financial repression, fixed income, framing effect, George Santayana, hindsight bias, Home mortgage interest deduction, index fund, invisible hand, Isaac Newton, John Bogle, Long Term Capital Management, loss aversion, margin call, market bubble, money market fund, mortgage tax deduction, new economy, Own Your Own Home, passive investing, Paul Samuelson, pets.com, Ponzi scheme, price stability, profit maximization, publish or perish, purchasing power parity, RAND corporation, random walk, Richard Thaler, risk free rate, risk tolerance, risk-adjusted returns, risk/return, Robert Shiller, Robert Shiller, short selling, Silicon Valley, South Sea Bubble, stocks for the long run, survivorship bias, the rule of 72, The Wisdom of Crowds, transaction costs, Vanguard fund, zero-coupon bond, zero-sum game

Next year, you also earn 10 percent on the $110 you start with, so you have $121 at the end of year two. Thus, the total return over the two-year period is 21 percent. The reason it works is that the interest you earn from your original investment also earns interest. Carrying it out in year three, you have $133.10. Compounding is powerful indeed. A useful rule, called “the rule of 72,” provides a shortcut way to determine how long it takes for money to double. Take the interest rate you earn and divide it into the number 72, and you get the number of years it will take to double your money. For example, if the interest rate is 15 percent, it takes a bit less than five years for your money to double (72 divided by 15 = 4.8 years).


pages: 386 words: 122,595

Naked Economics: Undressing the Dismal Science (Fully Revised and Updated) by Charles Wheelan

"Robert Solow", affirmative action, Albert Einstein, Andrei Shleifer, barriers to entry, Bear Stearns, Berlin Wall, Bernie Madoff, Bretton Woods, business cycle, buy and hold, capital controls, Cass Sunstein, central bank independence, clean water, collapse of Lehman Brothers, congestion charging, creative destruction, Credit Default Swap, crony capitalism, currency manipulation / currency intervention, Daniel Kahneman / Amos Tversky, David Brooks, demographic transition, diversified portfolio, Doha Development Round, Exxon Valdez, financial innovation, fixed income, floating exchange rates, George Akerlof, Gini coefficient, Gordon Gekko, greed is good, happiness index / gross national happiness, Hernando de Soto, income inequality, index fund, interest rate swap, invisible hand, job automation, John Markoff, Joseph Schumpeter, Kenneth Rogoff, libertarian paternalism, low skilled workers, Malacca Straits, market bubble, microcredit, money market fund, money: store of value / unit of account / medium of exchange, Network effects, new economy, open economy, presumed consent, price discrimination, price stability, principal–agent problem, profit maximization, profit motive, purchasing power parity, race to the bottom, RAND corporation, random walk, rent control, Richard Thaler, rising living standards, Robert Gordon, Robert Shiller, Robert Shiller, Ronald Coase, Ronald Reagan, Sam Peltzman, school vouchers, Silicon Valley, Silicon Valley startup, South China Sea, Steve Jobs, The Market for Lemons, the rule of 72, The Wealth of Nations by Adam Smith, Thomas L Friedman, Thomas Malthus, transaction costs, transcontinental railway, trickle-down economics, urban sprawl, Washington Consensus, Yogi Berra, young professional, zero-sum game

From 1975 until the mid-1990s, for reasons that are still not fully understood, productivity growth slowed to 1.4 percent a year. Then it got better again; from 2000 to 2008, productivity growth returned to a much healthier 2.5 percent annually. That may seem like a trivial difference; in fact, it has a profound effect on our standard of living. One handy trick in finance and economics is the rule of 72; divide 72 by a rate of growth (or a rate of interest) and the answer will tell you roughly how long it will take for a growing quantity to double (e.g., the principal in a bank account paying 4 percent interest will double in roughly 18 years). When productivity grows at 2.7 percent a year, our standard of living doubles every twenty-seven years.


The Simple Living Guide by Janet Luhrs

air freight, Albert Einstein, car-free, cognitive dissonance, Community Supported Agriculture, compound rate of return, financial independence, follow your passion, Golden Gate Park, job satisfaction, late fees, money market fund, music of the spheres, passive income, Ralph Waldo Emerson, risk tolerance, telemarketer, the rule of 72, urban decay, urban renewal, Whole Earth Review

At least open up a passbook savings or money market account at your bank while you are shopping for the best investment package. Remember, any investment is better than continually giving your money away to the tailor, the baker, and candlestick maker. Why line their pockets when you can line your own? To get yourself fired up about how much you can earn by investing, use the Rule of 72. This tells you how long it will take for your money to double. Divide 72 by the interest rate you are getting. If you earn 8 percent, your money takes 9 years to double (8 into 72 is 9). If you invest $5,000 at 10 percent, you divide 72 by 10, which yields 7.2 years. After 7.2 years you will have $10,000.


Principles of Corporate Finance by Richard A. Brealey, Stewart C. Myers, Franklin Allen

3Com Palm IPO, accounting loophole / creative accounting, Airbus A320, Asian financial crisis, asset allocation, asset-backed security, banking crisis, Bear Stearns, Bernie Madoff, big-box store, Black-Scholes formula, break the buck, Brownian motion, business cycle, buy and hold, buy low sell high, capital asset pricing model, capital controls, Carmen Reinhart, carried interest, collateralized debt obligation, compound rate of return, computerized trading, conceptual framework, corporate governance, correlation coefficient, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, cross-subsidies, discounted cash flows, disintermediation, diversified portfolio, equity premium, eurozone crisis, financial innovation, financial intermediation, fixed income, frictionless, fudge factor, German hyperinflation, implied volatility, index fund, information asymmetry, intangible asset, interest rate swap, inventory management, Iridium satellite, Kenneth Rogoff, law of one price, linear programming, Livingstone, I presume, London Interbank Offered Rate, Long Term Capital Management, loss aversion, Louis Bachelier, market bubble, market friction, money market fund, moral hazard, Myron Scholes, new economy, Nick Leeson, Northern Rock, offshore financial centre, Ponzi scheme, prediction markets, price discrimination, principal–agent problem, profit maximization, purchasing power parity, QR code, quantitative trading / quantitative finance, random walk, Real Time Gross Settlement, risk free rate, risk tolerance, risk/return, Robert Shiller, Robert Shiller, shareholder value, Sharpe ratio, short selling, Silicon Valley, Skype, Steve Jobs, sunk-cost fallacy, Tax Reform Act of 1986, The Nature of the Firm, the payments system, the rule of 72, time value of money, too big to fail, transaction costs, University of East Anglia, urban renewal, VA Linux, value at risk, Vanguard fund, yield curve, zero-coupon bond, zero-sum game, Zipcar

A 20-year annuity starting at $100 per year but declining at 5% per year. CHALLENGE 38. Future values and continuous compounding Here are two useful rules of thumb. The “Rule of 72” says that with discrete compounding the time it takes for an investment to double in value is roughly 72/interest rate (in percent). The “Rule of 69” says that with continuous compounding the time that it takes to double is exactly 69.3/interest rate (in percent). a. If the annually compounded interest rate is 12%, use the Rule of 72 to calculate roughly how long it takes before your money doubles. Now work it out exactly. b. Can you prove the Rule of 69?


pages: 825 words: 228,141

MONEY Master the Game: 7 Simple Steps to Financial Freedom by Tony Robbins

3D printing, active measures, activist fund / activist shareholder / activist investor, addicted to oil, affirmative action, Affordable Care Act / Obamacare, Albert Einstein, asset allocation, backtesting, Bear Stearns, bitcoin, buy and hold, clean water, cloud computing, corporate governance, corporate raider, correlation does not imply causation, Credit Default Swap, Dean Kamen, declining real wages, diversification, diversified portfolio, Donald Trump, estate planning, fear of failure, fiat currency, financial independence, fixed income, forensic accounting, high net worth, index fund, Internet of things, invention of the wheel, Jeff Bezos, John Bogle, Kenneth Rogoff, lake wobegon effect, Lao Tzu, London Interbank Offered Rate, market bubble, money market fund, mortgage debt, new economy, obamacare, offshore financial centre, oil shock, optical character recognition, Own Your Own Home, passive investing, profit motive, Ralph Waldo Emerson, random walk, Ray Kurzweil, Richard Thaler, risk free rate, risk tolerance, riskless arbitrage, Robert Shiller, Robert Shiller, salary depends on his not understanding it, San Francisco homelessness, self-driving car, shareholder value, Silicon Valley, Skype, Snapchat, sovereign wealth fund, stem cell, Steve Jobs, survivorship bias, tail risk, telerobotics, The future is already here, the rule of 72, thinkpad, transaction costs, Upton Sinclair, Vanguard fund, World Values Survey, X Prize, Yogi Berra, young professional, zero-sum game

After reading this book, you will learn a strategy that is based on Ray’s groundbreaking approach for the world’s wealthiest individuals, institutions, and governments. HOW FAST CAN YOU GO? It’s probably pretty obvious that we’d all like better returns. But what’s less obvious is the massive impact that better returns have on your time horizon for investing. The “rule of 72” says that it takes 72 years to double your money at a 1% compounded rate. So if you’ve got $10,000 to invest at 1% compounded, you may not be around to see that money double. You can cut that timeline in half by doubling your rate to 2%, and in half again by doubling that rate to 4%! So what’s the difference between a 10% return and a 4% return?


pages: 1,205 words: 308,891

Bourgeois Dignity: Why Economics Can't Explain the Modern World by Deirdre N. McCloskey

Airbnb, Akira Okazaki, big-box store, Black Swan, book scanning, British Empire, business cycle, buy low sell high, Capital in the Twenty-First Century by Thomas Piketty, clean water, Columbian Exchange, conceptual framework, correlation does not imply causation, Costa Concordia, creative destruction, critique of consumerism, crony capitalism, dark matter, Dava Sobel, David Graeber, David Ricardo: comparative advantage, deindustrialization, demographic transition, Deng Xiaoping, Donald Trump, double entry bookkeeping, en.wikipedia.org, epigenetics, Erik Brynjolfsson, experimental economics, Ferguson, Missouri, fundamental attribution error, Garrett Hardin, Georg Cantor, George Akerlof, George Gilder, germ theory of disease, Gini coefficient, God and Mammon, greed is good, Gunnar Myrdal, Hans Rosling, Henry Ford's grandson gave labor union leader Walter Reuther a tour of the company’s new, automated factory…, Hernando de Soto, immigration reform, income inequality, interchangeable parts, invention of agriculture, invention of writing, invisible hand, Isaac Newton, Islamic Golden Age, James Watt: steam engine, Jane Jacobs, John Harrison: Longitude, John Maynard Keynes: technological unemployment, Joseph Schumpeter, Kenneth Arrow, knowledge economy, labor-force participation, lake wobegon effect, land reform, liberation theology, lone genius, Lyft, Mahatma Gandhi, Mark Zuckerberg, market fundamentalism, means of production, Naomi Klein, new economy, North Sea oil, Occupy movement, open economy, out of africa, Pareto efficiency, Paul Samuelson, Pax Mongolica, Peace of Westphalia, peak oil, Peter Singer: altruism, Philip Mirowski, Pier Paolo Pasolini, pink-collar, Plutocrats, plutocrats, positional goods, profit maximization, profit motive, purchasing power parity, race to the bottom, refrigerator car, rent control, rent-seeking, Republic of Letters, road to serfdom, Robert Gordon, Robert Shiller, Robert Shiller, Ronald Coase, Scientific racism, Scramble for Africa, Second Machine Age, secular stagnation, Simon Kuznets, Social Responsibility of Business Is to Increase Its Profits, spinning jenny, stakhanovite, Steve Jobs, The Chicago School, The Market for Lemons, the rule of 72, The Spirit Level, The Wealth of Nations by Adam Smith, Thomas Malthus, Thorstein Veblen, total factor productivity, Toyota Production System, Tragedy of the Commons, transaction costs, transatlantic slave trade, Tyler Cowen: Great Stagnation, uber lyft, union organizing, very high income, wage slave, Washington Consensus, working poor, Yogi Berra

Unless one believes in mercantilist/business-school fashion that a country must “compete” to prosper from world betterment, even the leaky boats of the Phelpsian undynamic countries will rise. To appreciate what will happen in the world’s economy over the next fifty or a hundred years it’s a good idea to pause to learn the “Rule of 72.” The rule is that something (such as income) growing at 1 percent per year will double in seventy-two years. The fact is not obvious without calculation. It just happens to be true. You can confirm it by taking out your calculator and multiplying 1.01 by itself seventy-two times. It follows that if the something grows twice as fast, at 2 percent instead of 1 percent, that something will double, of course, in half the time, thirty-six years—as a runner going twice as fast will arrive at the mile marker in half the time.