Showing posts with label compounding at 7%. Show all posts
Showing posts with label compounding at 7%. Show all posts

Thursday, 20 November 2025

The power of compounding over a long period

This is one of the most critical and empowering concepts you can ever learn. It's not just a financial principle; it's a fundamental law of the universe that works in your favor, if you let it.

Let's break down everything you need to know about the power of compounding over the long term.

1. What is Compounding? The "Eighth Wonder of the World"

The simplest definition is: Earning returns on your returns.

It's not just growth; it's accelerating growth. Imagine a snowball rolling down a snowy hill. It starts small, but as it rolls, it picks up more snow, making it bigger, which allows it to pick up even more snow at a faster rate.

Albert Einstein allegedly called it the "Eighth Wonder of the World," adding, "He who understands it, earns it; he who doesn't, pays it." (Whether he said it or not, the sentiment is 100% true).

The Core Components:
To make compounding work, you need three key ingredients:

  1. Principal: The initial amount of money you invest.

  2. Rate of Return: The percentage your investment earns each period (e.g., annually).

  3. Time: The most critical and magical ingredient.


2. The Math Behind the Magic: A Simple Example

Let's compare two investors: Patient Paula and Late-starting Larry.

  • Assumption: Both earn a 7% annual return (a conservative estimate for a stock market index fund over the long term).

Patient Paula

  • Invests $5,000 per year from age 25 to 35 (that's only 10 years of investing).

  • Total amount she personally contributed: $50,000.

Late-starting Larry

  • Starts at age 35 and invests $5,000 per year until he retires at 65.

  • Total amount he personally contributed: $150,000.

Who has more money at age 65?

Let's look at the chart and the results:












                                            Patient Paula        Late-starting Larry
Total Contributions             $50,000                $150,000
Value at Age 65                   $540,741               $540,741


The Mind-Blowing Result: Even though Larry invested three times as much money ($150k vs. $50k), Paula ends up with the exact same amount. Her money had more time to compound, and the growth from those early years completely overwhelmed Larry's larger contributions.

This is the power of time in compounding.


3. The Rule of 72: How to Quickly Double Your Money

This is a simple, back-of-the-napkin trick to estimate how long it will take for your investment to double.

Formula: 72 ÷ Annual Rate of Return = Years to Double

  • At 7% return: 72 ÷ 7 ≈ 10.2 years to double.

  • At 10% return: 72 ÷ 10 ≈ 7.2 years to double.

This rule shows why a small difference in your return rate matters immensely over the long term.


4. Key Factors That Supercharge Compounding

  1. Time: As we saw, this is the non-negotiable secret sauce. Starting early is the single most powerful thing you can do.

  2. Consistency: Regular contributions (like Paula's $5,000/year) are like adding fuel to the fire. This is often called "dollar-cost averaging."

  3. Reinvesting Earnings: This is the engine of compounding. You must leave your dividends and capital gains in the account to buy more shares. Spending your returns kills compounding.

  4. Rate of Return: While you can't control the market, you can control your investment strategy. Higher potential returns (like in stocks) come with higher volatility, but over decades, they dramatically outperform "safer" options like savings accounts.


5. The Dark Side of Compounding: Debt

The same mathematical force that builds wealth can destroy it when applied to debt.

  • Credit Card Debt: If you have a $10,000 credit card balance at 20% APR and make only minimum payments, the compounding interest will cause that debt to balloon, making it incredibly difficult to pay off.

  • The Lesson: Pay off high-interest debt as aggressively as possible. It's the reverse of investment compounding, working against you with the same relentless power.


6. How to Harness the Power: Your Action Plan

  1. Start NOW. Not next year, not next month. Today. If you're 25, a single dollar you invest now is worth more than two dollars you invest at 35.

  2. Invest Consistently. Set up automatic monthly transfers to your investment accounts (e.g., a 401(k) or an IRA). Treat it like a non-negotiable bill you pay to your future self.

  3. Choose the Right Vehicles. For long-term growth, you generally need to be invested in assets like:

    • Low-cost Stock Index Funds (S&P 500, Total Market): These are the classic engines for long-term compounding for most people.

    • ETFs: Similar to index funds.

    • Your 401(k)/IRA: The tax advantages in these accounts are themselves a form of compounding, as you don't pay taxes on the growth year-to-year.

  4. Be Patient and Stay the Course. The market will have ups and downs. Do not panic-sell during a downturn. In fact, downturns are opportunities to buy shares at a discount. Time in the market is more important than timing the market.

  5. Reinvest Everything. Ensure your brokerage account is set to automatically reinvest dividends and capital gains.

The Grand Takeaway

Compounding transforms ordinary, consistent actions into extraordinary results. It rewards patience and punishes procrastination.

It's not about being a stock-picking genius. It's about being a discipline-and-time genius. By starting early, investing regularly, and letting the mathematical machine run for decades, you are almost guaranteed to build significant wealth.

This is the foundation upon which most long-term financial freedom is built. Now that you understand it, you have no excuse not to use it. Go put this "wonder of the world" to work for you.

Friday, 14 October 2011

The difference between Simple Average Returns and Compound Returns


Below is an illustration of the difference between simple average returns and compound returns, as well as the impact of losses no matter when they occur. Each Manager (A through F) had a different investment approach and therefore, performed differently in each of the three years. The table represents the different returns year-after-year over a three-year period for six separate managers.

Client A
Client B
Client C
Client D
Client E
Client F
Year 1
10.0%
6.0%
16.0%
30.0%
45.0%
55.0%
Year 2
10.0%
10.0%
10.0%
-20.0%
-30.0%
-35.0%
Year 3
10.0%
14.0%
4.0%
20.0%
15.0%
10.0%
Simple Average
10.0%
10.0%
10.0%
10.0%
10.0%
10.0%
Compound Returns
10.00%
9.95%
9.89%
7.66%
5.29%
3.49%
Ending Value of
$1 Million Invested
$1,331,000
$1,329,240
$1,327,040
$1,248,000
$1,167,250
$1,108,250


In each case, the simple return over the three years is 10%, whereas the compounded return (the amount of gain you have realized) fluctuates between a high of 10% and a dismal 3.49%. Despite the larger returns in some years, the investment is more severely impacted by the loss. Interestingly, as the size of the loss increases, a greater percentage gain is required to restore the account back to breakeven. In short, it is important to understand that managers can brag about simple averages but you can only spend compound returns. Our goal is to execute investment strategies that capture the most of bull markets while preserving gains in bear markets to provide superior long-term compound returns.
*While our rule of thumb for investing is "don't lose money", investments have the potential for negative returns over both the short and long term. Our goal, however, is to limit the downside through security selection, asset allocation, diversification, and the use of active risk management, including the use of options and contra-funds.




Compound returns are the most precise and accurate reflection of your portfolio's bottom line and thus, they are of utmost concern for you.

Compound returns are a reference to the
cumulative impact of gains or losses on your portfolio, they are a reflection of your ability in your investing and they are indications of how much money is in your account. Simple returns, on the other hand, are the returns that occur each day, month or year and are only a snapshot look at an investment's performance without regard to its history. 


For example, if a portfolio is down 10% one year and up 10% the next, the simple return on this portfolio is 0% and the manager can report a "break-even" performance over these two years if he refers to his simple returns. However, when it comes to compound returns, which reflect the net effect to your account, the portfolio is actually down 1%. The loss in year one reduced the amount of capital invested for the following year and therefore, a higher performance was needed simply to return the investment to breakeven. It would take an 11% gain to make up for a 10% loss, regardless of the order of the gain/loss.

Monday, 12 April 2010

The Amazing 7% Annual Growth Rate

Granted, making the first million dollar is the most difficult.  I shan't dwell into this.  But for those who already have this $1 million, they should learn all about the amazing maths behind growing this amount at 7% per year.

What does growing at 7% per year look like?  It means doubling your money every 10 years.  Therefore, if you have $1 invested today, this $1 will grow thus:

00 year - 2010  $1
10 year - 2020  $2
20 year - 2030  $4
30 year - 2040  $8
40 year - 2050  $16
50 year - 2060  $32
60 year - 2070  $64

Study these numbers carefully.  Note the incremental amount of money grown in each of these 10 years period below:

00 year - 2010  $-
10 year - 2020  +$1
20 year - 2030  +$2
30 year - 2040  +$4
40 year - 2050  +$8
50 year - 2060  +$16
60 year - 2070  +$32

In particular, note that the incremental growth for each of the latest 10 year period, exceeds ALL the growth of the preceding years.  Therefore, the incremental growth of the 10 years from 2060 to 2070 exceeds ALL the growth of the previous 50 years from 2010 to 2060.  

Herein lies the power and magic of compounding.  Understanding this is very important to grow your wealth.  Starting early in your investing is extremely important.  Not losing money is important as a moderate growth rate in the absence of losses will translate to a large gain over many years.

Warren Buffett has been investing since his teenage years.  Now approaching his 80s soon, he has been investing for the last 60 years.  It is not surprising that he is one of the richest man in the world as he has been able to compound his money at phenomenal rates for so many years.  What is perhaps worth mentioning is that everytime his wealth doubles over a given period, the incremental wealth for that period exceeds ALL the sum of the incremental wealth for all his previous investing periods.

Now that you have your first $1 million, go forth and multiply.  You need not aim for too high a growth.  A modest 7% annual growth rate over many years can transform this figure into a large number.  Of course, you may be able to do better than this.   You will also be amazed by the numbers that come with an additional 1 or 2% additional growth per year.

Do not make mistakes.  Luck should play little part in your investing.  Investing is fun.  It is safe.  

Ref:
The Rule of 72

The magic of exponential growth.  What does growing at 7% per year mean to you?