Maximize the power of compounding

After minimizing expenses, capital loss, and the risk of capital loss, we need to maximize gains. The best way to do this is to use the power of compounding.

What is compounding?
Compounding is the concept of adding interest back to principal, so that interest is earned on interest from that moment on. For example, $100 at 10% interest rate will result in $10 interest ($100 x 10%) after the first year. For the second year, the 10% interest is calculated on $110 ($100 + $10), resulting in $11 interest ($110 x 10%) in the second year.

So how do you calculate how much money will you have in the future? You need to calculate future value.

Calculating "simple" compound interest
The basic formula for calculating the time value of money in a compound interest situation is as follows:

FV = PV * ( 1 + r ) ^ n

FV: future value (the amount of money you will have in the future)
PV: present value (the amount of money you contribute/invest at present time)
r: annual rate of return (the rate of return on your investments)
n: number of time periods (the number of years you let your investments compound)

Let's say you invested $1,000 today and earned a return of 8% p.a., in 30 years you will have:
FV = $1,000 * (1 + 8%) ^ 30
= $1,000 * (1.08^30)
= $1,000 * 10.0626569
= $10,063 (more than 10 times your invested capital!)

Please note that this formula calculates the "simple" compound interest, where you make a one-off investment (the present value) and the investment earns a steady rate of return (r) over a number of years (n) until maturity. In order to calculate "accumulative" compound interest for, say, the contributions you make year-after-year to your retirement fund, you can use a spreadsheet to help you with the calculation.

Calculating "accumulative" compound interest
To calculate "accumulative" compound interest, your will need a spreadsheet with 5 columns:

• [Column A] Year Number: This column is just for you to keep track of the year number, listing from one to [whatever number you choose] in ascending order.
• [Column B] Start of Year: The formula here is equal to "End of Year" value (e.g. in cell B3, enter "=E2") for the previous year, except for the first year, which should be zero.
• [Column C] Return for the Year: The formula is "Start of Year" multiplied by rate of return (e.g. in cell C3, enter "=B3*8%").
• [Column D] Contribution: You should state the amount you contribute each year in this column.
• [Column E] End of Year: The formula is "Start of Year" + "Return for the Year" + "Contribution" (e.g. in cell E3, enter "=B3+C3+D3").

I have created a spreadsheet on Google Docs that you can use to calculate "simple" compound interest and "accumulative" compound interest. Just fill in the variables in yellow and the formula will make the calculations. I have also included the spreadsheet that I used to calculate the numbers for the "Luke vs Evan" example at the end of this post.

How to maximize the power of compounding?
There are a few variables that you can maximize to increase the amount of wealth you accumulate:

• The rate of return on your investments.
• The amount you contribute now.
• The number of years you let your investments compound.

Let us start with the base scenario that if you contribute $1,000 per year for 30 years and earn a return of 8% p.a., you will have $122,346 in 30 years.

Increasing the rate of return
You will have significantly higher wealth in the future even with a small increase in rate of return. By increasing your rate of return by 2%, your wealth will grow in 30 years to $180,943 at 10% return, a 48% increase from the $122,346 you will have with an 8% return. This approach, however, is limited by how high a rate of return you can realistically obtain without involving significant risks of capital loss.

If you invest in a no-load index fund with low management expense ratio and reinvest all dividends, it is possible to achieve a long-term return of 6-8% (assuming the long-term stock return will be 5-6% with 1-2% dividend yield). While it may be possible to outperform the market, it is very difficult to do so in the long run. Some have outperformed the market over a long period of time, a few that come to mind are Warren Buffett of Berkshire Hathaway, Marty Whitman of Third Avenue Fund, and the team at Tweedy, Browne. All of them are very good value investors - investors who buy assets at a discount to the their intrinsic values.

Even if you are able to invest with very good investment managers (perhaps yourself, if you are that good), I would cap the rate of return assumption at 15%. When doing my own financial planning, I tend to be conservative and assume a return of 6-8% p.a. I would rather be conservative in my planning than risk missing the target return rate and falling behind in my quest for financial independence.

Increasing contributions
By increasing the amount you contribute and invest, you will significantly increase your future wealth. Every dollar you invest now will compound and grow exponentially. Your standard of living may not be affected much now by saving an additional $1,000 per year, but the additional $122,346 you will have in 30 years may make a substantial difference in your standard of living in the future.

This approach is limited by how high your income is and how low your expenses are, but this is the variable that you can exert the most control. While it may be difficult to increase your income significantly very quickly, it is relatively easy to reduce living expenses within a short period of time. The key to maximizing your present contributions is to be thrifty and minimize expenses.

Increasing the length of time
By increasing the length of time you let your money compound, you will increase your future wealth exponentially. At 8% return, $1,000 per year will accumulate to $15,645 in 10 years, $49,423 in 20 years, $122,346 in 30 years, and $279,781 in 40 years.

This approach is limited by how much time do you have until retirement. The key to maximizing this variable is by starting now - not next quarter, not next year, but now. With compound interest working its magic and growing your investments exponentially, you should invest as much as possible and for as long as possible!

Why start now?
Let us imagine two brothers graduated from college when they were 22 years old, and they worked 45 years until their full retirement age of 67. Luke was a late accumulator of wealth and contributed $2,500 to his retirement fund for the last 30 years he worked. Evan was an early accumulator of wealth and contributed $2,500 per year to his retirement fund for the first 15 years he worked. Let us assume that both earned a consistent 8% return on their retirement funds. How much will they have contributed and how much will they have when they retire?

Luke would have $305,865 from his contribution of $75,000. Evan would have contributed half as much as Luke ($37,500), but he would have ended up with 2.4 times more than Luke - $737,700. To come close to the level of Evan's retirement fund, Luke will to contribute $6,000 per year (total contribution of $180,000) to have $734,075 by retirement. The best thing both of them could have done was to be like their friend, Calvin, a consistent accumulator of wealth. Calvin contributed $2,500 per year from year 1 until retirement and would have $1,043,565 from his contribution of $112,500, much more than they each have.

Playing catch up against the power of compounding is a very difficult and expensive endeavor. The best thing you can do is to start now, be thrifty, minimize expenses, contribute as much as possible, invest consistently, and let the power of compounding work its magic.

Related posts:

• Pay yourself first.
  
• Minimize expenses.
• Minimize expenses (revisited).
  
• Minimize capital loss.
  

References:

• Compound Interest Calculator on Google Docs.
• Wikipedia: Time Value of Money and Compound Interest.
  
• Berkshire Hathaway.
  
• Third Avenue Funds.
  
• Tweedy, Browne Company LLC.
  

## This post is part of "The Principles of Wealth Accumulation" series on this blog.

P.S. This post was featured in The 84th Festival of Stocks at Value Investing, and a Few Cigar Butts.

Disclosure: Long BRK.B.