Over the next few weeks, whilst the blog is on a break, I am posting some older articles that new readers may not have gotten a chance to read. This one originally posted in May 2018.
Compound growth in action
If I offer you one million dollars cash now or 1 cent that doubles in value every day for a month, which would you choose and why? The one million dollars looks like the best option at first glance. The answer may surprise you though. Look at the results below of one cent doubled for 30 days.
Day 1 1 cent
Day 2 2 cents
Day 3 4 cents
Day 4 8 cents
Day 5 16 cents
Day 6 32 cents
Day 7 64 cents
Day 8 $1.28
Day 9 $2.56
Day 10 $5.12
Day 11 $10.24
Day 12 $20.48
Day 13 $40.96
Day 14 $81.92
Day 15 $163.84
Day 16 $327.69
Day 17 $655.36
Day 18 $1,310.72
Day 19 $,2621.44
Day 20 $5,242.88
Day 21 $10,485.76
Day 22 $20,971.52
Day 23 $41,943.04
Day 24 $83,886.08
Day 25 $167,772.16
Day 26 $335,544.32
Day 27 $671,088.64
Day 28 $1,342,177.28
Day 29 $2,684,354.56
Day 30 $5,368,709.12
If you chose the doubling cent, on day 24 it is not looking like a good decision. But look what happens from day 25 onwards. The jump in value in the last 5 days of the month is significant. If we add a 31st day to the month, then our 1 cent will now be worth almost 11 million dollars. This is the magic of compounding.
Although this is an incredible example, sadly it is just an example. I don’t know of any investment that can double your money every day for a month. But there are lessons we can learn from this example.
LESSONS OF COMPOUND INTEREST
Lesson number 1: Returns matter
The numbers in the 30-day example are so great because of a high rate of return – 100%. The same theory applies to lower, more realistic rates of return though. Let’s have a look at investing for a 40-year period. In the table below are different rates of return for an investment of $5,000 per year.
After inflation returns
2%
3%
4%
5%
6%
7%
8%
9%
10%
40-year returns
$308,050
$383,316
$494,132
$634,199
$820,238
$1,068,048
$1,398,905
$1,841,459
$2,434,259
You will see that percent changes in our rate of return can make a big difference. If we can go from a 4% return to a 7% return, we will more than double our 40-year return from $494,000 to over one million. Finding an investment that charges 1% less in fees with similar results can make a difference of $100,000 or more.
Lesson number 2: Time matters
The amount of time we invest matters. If, in the 30-day example, we stopped investing after day 20, we would have only $5,000. It was not until day 26 that we started seeing real progress towards 1 million dollars. That extra 4 days at the end is significant. Time matters. The power of compound interest is driven by the rate of return and how long we can get the returns.
Let’s take the same example from lesson 1 where we were investing $5,000 per year. This time we will assume just one rate of return of 7%. The variable will be the length of time we are invested.
Returns
$73,918
$219,326
$505,365
$1,068,048
$2,174,930
Length of time invested
10 years
20 years
30 years
40 years
50 years
In this example, each extra 10 years invested results in over double our returns. An extra 20 years is over triple the returns. This is because as our cash pile gets bigger, our interest returns get greater, whilst our own contributions remain the same. We are contributing the same amount of money but getting higher and higher returns as time goes on. More bang for our buck.
Lesson number 3: In the beginning, it is easy to give up
On day 15 of the doubling cent example we only had $163.84. What do most people do with $163.84? We spend it. It doesn’t seem like enough money to make any real investment returns. When we withdraw the money though, we must start back at day one. It will take another 15 days to get back to $163.84 again. Whereas, if we left the money for another 15 days instead of taking it out – 5 million dollars. Both scenarios we are invested for 30 days yet there is a huge difference in the end result. The only difference is we spent our returns at the halfway point. Don’t disregard the insignificance of small amounts because small amounts turn into large amounts over time.
I know it is difficult at the beginning because we are not seeing big returns. 10% return on $500 is just $50. Whereas the same 10% return on $100,000 is $1,000. Do not scoff at the $50, because one day that $50 return will become a $1,000 return if you keep at it.
Lesson number 4: In the beginning, the amount you save matters more than the interest rate
In the beginning, the most important thing is just beginning. Too often people are scared to make investments because they worry about the returns. Or maybe they are trying to time the market and buy when shares are cheaper. Returns are basically irrelevant in the beginning when we have little money invested. If we have $1,000 to invest and see a return of 10%, we will get $100. If we see a return of just 4%, we will get $40. All the time we spent fretting about when and how to invest only cost us $60 with a huge 6% difference in returns. Returns do not matter at the beginning as much as the amount we save.
If we invested straight away though, we could have made our $60 back and then some. $60 at a 7% rate of return will be $900 in 40 years. The key is to just get started and invest as much as we can afford. Waiting will cost time and money.
Lesson number 5: In the end, the interest rate matters more than the amount you save
Unlike the beginning, later in life we should have more money invested. The more money we have, the more return for our money we will get. And the more changes in the rates of return matter.
Let’s say we are now 55 years old with $500,000. Invested for 40 years at a 2% rate of return will see us with 1.1 million dollars. If the return was 7%, our return will be 7.5 million dollars. This example assumes we are not spending this money in retirement, which is not realistic. I have used this example to highlight the power of changes in interest rates when we have more money.
The common advice in our later years is to invest our money in low risk investments such as bonds or savings. But, this generic advice could be costing us a lot of money, or causing us to outlive our savings. This advice is suitable to some, but definitely not to all. Seek advice from a professional who can assess your own personal situation.
FINAL THOUGHTS
For the majority, compounding interest is not the result of a lotto win or an inheritance. It is the result of consistent, small contributions over a long period of time. The longer we delay, the more effort is required to achieve the same result. It is easy to get discouraged at the beginning where the results of our efforts are barely visible. Do not let this deter you though. Over time, the gains from our contributions will get incrementally larger and larger.
Invest wisely. Yes, interest rates matter. But this doesn’t mean to go chasing risky 15% returns. There are ways to get good returns whilst still minimising our exposure to too much risk.
Don’t let the charts discourage you either if you are behind. Some compounding is still better than no compounding. There is little point in throwing our arms in the air and saying it is too late. Wherever we are, the best time to start is now. One extra year of saving or one extra year of work at the end of our savings accumulation can make all the difference. Compounding is a powerful force and it is much better having it work for us than against us.
The information contained on this site is the opinion of the individual author(s) based on their personal opinions, observation, research, and years of experience. The information offered by this website is general education only and is not meant to be taken as individualised financial advice, legal advice, tax advice, or any other kind of advice. You can read more of my disclaimer here
Comment below. How did you learn about the effect of compound interest? Do you have any other lessons of compounding you can add to my list?