**Compounding is the 8 ^{th} Wonder of the World said Einstein**

**Mohnish Pabrai Lecture at Peking University (Guanghua School of Mgmt) – Dec 22, 2017**

**Mohnish Pabrai Presentation on Compounding**

**CFI@ISB – Compounding is the 8 ^{th} wonder of the world – Mr. Mohnis Pabrai**

1. Compound Interest can **work for you** or **work against you**.

If you want your money to work for you in your future, I would recommend you to listen carefully to what Mohnish Pabrai says about the compound interest, which Einstein called is the 8^{th} wonder of the world.

If you can fully internalize what he said and apply it for yourselves, it will benefit you in your life.

It is vitally important to understand the concept of Compound Interest. Compounding can **work for you** or **work against you**. If you owe people money, like credit cards, student loan, personal loan, payday loan, high mortgages, etc it will work equally against you. So, “getting rid of debts first” is of utmost priority. It is equally important to better yourself so that you have the skills to earn money first. That is the correct direction. But whenever you want a diversion from your study, spend a little time understanding about compound interest and money matters [financial accounting].

Mohnish Pabrai gave examples of the cost of compounding when one spends money to buy a Tesla car or even to drink Starbuck coffee or wine everyday. This is investing in depreciating assets, where the compounding will **work against you**. To avoid debt he said that there should be a life style change.

Most of us do not understand what the power of compounding means to us. Initially the compounding does not appear to be very significant. But the **exponential growth** of compounding comes at the later years and when the rate of return is also high. The **real magic** of compounding kicks in then. For example, with a $1,000 investment on a 10% return over 63 years will only grow to **$405,265/,** but with a 20% return, the investment will grow to a **staggering $97,368,505/.**

I have worked out what is the power of Compounding below:

In the annual report of 1998, Warren Buffett stated the following:

*Over the 63 years, the general market delivered just under a 10% annual return including dividends. That means $1000 would have grown to $405,000 if all income had been reinvested. A 20 % rate of return, however, would have produced $97 million. That strikes us as statistically-significant differential that might, conceivably, arouse one’s curiosity*. (

*The Essay of Warren Buffett,3*selected and arranged by Lawrence A Cunningham, pg 92).

^{rd}Edition,I was curious and worked out the compound interest and found it to be

**accurate**. Most of us just can’t imagine this power of compounding!

Compound Interest, FV = PV (1+i)^n where

FV = Future Value, PV = $1,000/ (say), i = Rate of return, n = Years

n | |||||||

i | 5% | 7% | 8% | 10% | 15% | 20% | |

5 years | $1,276 | $1,403 | $1,469 | $1,611 | $2,011 | $2,488 | |

10 | 1,629 | 1,967 | 2,159 | 2,594 | 4,046 | 6,192 | |

15 | 2,079 | 2,759 | 3,172 | 4,177 | 8,137 | 15,407 | |

20 | 2,653 | 3,870 | 4,661 | 6,727 | 16,367 | 38,338 | |

25 | 3,386 | 5,427 | 6,848 | 10,835 | 32,919 | 95,396 | |

30 | 4,322 | 7,612 | 10,063 | 17,449 | 66,212 | 237,376 | |

40 | $7,040 | $45,259 | $ 267,864 | $1,469,772 | |||

50 | $11,467 | $117,391 | $ 1,083,657 | $9,100,438 | |||

63 | $405,265 | $ 6,667,514 | $97,368,505 | ||||

Charlie Munger states the following:**”Understanding both the power of compound return and the difficulty of getting it is the heart and soul of understanding a lot of things.” **The success of sit on your ass investing is driven by a company’s ability to

**shareholder equity at an**

__successfully compound__**over**

__attractive rate__**—**

__the long-term__**and it’s**

__if this isn’t possible, the strategy won’t work__**to**

__easier__**.**

__buy low and sell high__*“Over the long term, it’s hard for a stock to earn a much better return than the business which underlies it earns.*

**If the business earns 6% on capital over 40 years and you hold it for that 40 years, you’re not going to make much different than a 6% return–**__even if you originally buy it at a huge discount__.**Conversely,**__if a business earns 18% on capital over 20 or 30 years, even if you pay an expensive looking price, you’ll end up with a fine result.”__

**3. The Rule of 72**

Ifyou want to be able to do a **rough compound interest** problem **in your head**, use the rule of 72. The “**Rule of 72**” is a simplified way to determine how long an investment will take to double, given a fixed annual rate of interest. It is a very useful skill to have because it gives you a **lightning fast benchmark** to determine how good (or not so good) a potential investment is likely to be.

**The formula is:**

**Y = 72 / r** and **r = 72 / Y**

where Y and r are the years and interest rate, respectively.

The rule says that to find the number of years required to double your money at a given interest rate, you just divide 72 by the interest rate.

For example, if you want to know how long it will take to double your money at 10%, divide 72 by 10 and you get roughly 7 years. OR if you want to know the percentage of interest you need to get to double your money in 5 years, divide 72 by 5 and get roughly 15%.

The “rule” is remarkably accurate, as long as the interest rate is less than about twenty percent; at higher rates the error starts to become significant.

The rule of 72 states that $1 invested at 10% would take 7.2 years ((72/10) = 7.2) to turn into $2. In reality, a 10% investment will take 7.3 years to double ((1.10^7.3 = 2).

When dealing with low rates of return, the Rule of 72 is fairly accurate. This chart compares the numbers given by the rule of 72 and the actual number of years it takes an investment to double.

Rate of Return | Rule of 72 | Actual # of Years | Difference(#) of Years |

2% | 36.0 | 35 | 1.0 |

3% | 24.0 | 23.45 | 0.6 |

5% | 14.4 | 14.21 | 0.2 |

7% | 10.3 | 10.24 | 0.0 |

9% | 8.0 | 8.04 | 0.0 |

12% | 6.0 | 6.12 | 0.1 |

25% | 2.9 | 3.11 | 0.2 |

50% | 1.4 | 1.71 | 0.3 |

72% | 1.0 | 1.28 | 0.3 |

100% | 0.7 | 1 | 0.3 |

https://www.investopedia.com/ask/answers/what-is-the-rule-72/

Notice that, although it gives a quick rough estimate, the rule of 72 gets less precise as rates of return become higher.

**4. ****Doubling time **

** Doubling time** is the amount of **time** it takes for a given quantity to double in size or value at a constant growth rate.

The formula is y^x means to multiply y by itself x times.

This formula is very useful to remember and apply.

2^1 = 2×1 = 2

2^2 = 2×2 = 4

2^3 = 2x2x2 = 8

2^4 = 2x2x2x2 = 16

2^5 = 2x2x2x2x2 = 32

2^6 = 2x2x2x2x2x2 = 64

2^7 = 2x2x2x2x2x2x2 = 128

2^8 = 2x2x2x2x2x2x2x2 = 256

2^9 = 2x2x2x2x2x2x2x2x2 = 512

2^10 =2x2x2x2x2x2x2x2x2x2 =1024 = 1000 [say for easy to remember]

For example, if you **start** with an investment of **$1,000/**, and if you want to **grow **your investment **to $1,000,000/,** you will need 10 periods of x% rate of return.

At **10%** rate of return, by using the rule of 72 you need roughly 7 years [72/10 = 7.2]. And 10 periods of 7 years is **70 years** [10 x 7 years = 70 years].

At **12%** rate of return, by using the rule of 72 you need roughly 6 years [72/12 = 6.0]. And 10 periods of 6 years is **60 years** [10 x 6 years = 60 years].

At **15%** rate of return, by using the rule of 72 you need roughly 5 years [72/15 = 4.8]. And 10 periods of 5 years is **50 years** [10 x 5 years = 50 years].

At **20%** rate of return, by using the rule of 72 you need roughly 4 years [72/20 = 3.6]. And 10 periods of 4 years is **40 years** [10 x 4 years = 40 years].

At **26% **rate of return, by using the rule of 72 you need roughly 3 years [72/26 = 2.8]. And 10 periods of 3 years is **30 years** [10 x 3 years = 30 years].

At **36%** rate of return, by using the rule of 72 you need roughly 2 years [72/36 = 2.0]. And 10 periods of 2 years is **20 years** [10 x 2 years = 20 years].

5. **Buying Shares—Basic Principles to Remember**

You should try “getting rid of debts first”—as quickly as you possibly can. Once you have some savings, then you should look at how to make the GOOD companies [companies that give a high sustainable rate of return] work for you by investing in them when their prices have come down significantly. This great discount can come about once every 9 to 12 years. “In the forty-seven years that Warren Buffett has run Berkshire Hathaway, the company’s stock has **fallen roughly 40 percent to 50 percent at four different times**. We will identify three of those episodes—1973–1974 [Arab oil embargo], 1987–1988 [financial crisis], and 2007–2008 [sub-prime crisis]—and move on to the other perpetrator, the Internet bubble [2000-2001].” (p. 204, *Tap Dancing to Work*)

Warren Buffett and Charlie Munger said, “Buy great companies at a fair price rather than fair companies at a great price” [big discount]. See my article **Buying Shares—Basic Principles to Remember**. Remember if you do not START to do your home-work and understand what businesses you are investing in, you will **definitely lose your hard earned money**. A sure way to **gamble your money away is to buy shares without doing your homework. **

Understanding investing takes a great due of effort and time but you have to start sometime and the earlier you know the subject the better it is for you.

**6. F**

__ind a few outstanding companies, buy them, and hold them forever__ Ultimately, if you have the opportunity to find one or two outstanding companies with a sustainable rate of return of some **20%** **or more**, buy them big and hold them forever. Don’t ever sell them.

**Basically, you make few investment, very big investment, infrequent investment, and you make investment when the investment is in your favor.**

**7. Credit Cards Debt**

Do you know how much the credit card charges you in Singapore? The credit card charges interest on a **daily basis and compounded**. It also charges for late payment, minimum payment charges, annual card fees and overseas transaction fees. All these charges come to a **fantastic** and **scary** charge of between **26 to 28% per annum**. (see https://www.valuepenguin.sg/6-hidden-credit-card-fees-singapore-you-should-be-aware) Here is **how compound interest works against you**!!! So, **pay in full your monthly credit card bill.** Remember, always to get rid of your credit card debt first.

**8. Buying Shares without using a Calculator**

According to Mohnish Pabrai by the time Warren Buffett was 11 years old, he understood about Compound Interest. He uses the Rule of 72 and the Doubling Time Rule to invest. Thus he does not have to use a calculator to invest. He can do the Maths mentally. We can do the same.

No. of years to **double** **investment** = No. of period to double **multiply** by amount invested

For example, if the investment is $500,000/ and the rate of return is **15%**, then:

72/15 = about 5 years [one period]. So,

In **5 years** [one period], the $500,000/ amount invested will become **$1,000,000/** [2^1 = 2 x $500,000/]

In **10 years** [2 periods], the $500,000/ amount invested will become **$2,000,000/** [2^2 = 4 x $500,000/]

In **15 years** [3 periods], the $500,000/ amount invested will become **$4,000,000**/ [2^3 = 8 x $500,000/]

If the investment is $500,000/ and the rate of return is **12%**, then:

72/12 = 6 years [one period]. So,

In **6 years** [one period], the $500,000/ amount invested will become **$1,000,000/** [2^1 = 2 x $500,000/]

In **12 years** [2 periods], the $500,000/ amount invested will become **$2,000,000/** [2^2 = 4 x $500,000/]

In **18 years** [3 periods], the $500,000/ amount invested will become **$4,000,000/** [2^3 = 8 x $500,000/]

If the investment is $500,000/ and the rate of return is **8%**, then:

72/8 = 9 years [one period]. So,

In **9 years** [one period], the $500,000/ amount invested will become **$1,000,000/** [2^1 = 2 x $500,000/]

In **18 years** [2 periods], the $500,000/ amount invested will become **$2,000,000/** [2^2 = 4 x $500,000/]

In **27 years** [3 periods], the $500,000/ amount invested will become **$4,000,000/** [2^3 = 8 x $500,000/]

When Warren Buffett was 50 plus years old, he leant from Charlie Mumger that it is **far superior to buy** a wonderful company [that gives wonderful return] at a fair price than to buy a fair company [that gives mediocre return] at a wonder price [great discount]. Most of the $84 billion Warren makes comes from investing in 10 to 15 wonderful companies and holding them for a long, long time!!!