You’re looking at your bank accounts online and wondering how on earth you’ll get to retire, let alone achieve financial independence early.

After doing some research, the number 1,000,000 keeps popping up on your screen. “One million dollars?,” you keep muttering to yourself. “How can I ever save that much money?”

The good news is that you don’t have to. You can get your money to work for you by placing it in investment accounts and earning a return. Your old money will eventually earn more money on its own, thanks to the wonders of compound interest. No overtime is required.

Compound interest is something that Albert Einstein once referred to it as the “eighth wonder of the world.”

Those are some profound words for the boring interest you earn in your account, right?

Most people don’t understand how compound interest works, because it is not intuitive.

Today’s lesson is all about compound interest and its magical ability to turn a dusty small pile of cash into a beautiful barrel of retirement dollars, given a long enough time horizon.

Keep reading to find out.

- Compound Interest and the “Snowball Effect”
- How Simple Interest Works
- How Compound Interest Works
- Comparison: Simple vs Compound Interest
- Factors that Affect Compound Interest
- The Compound Interest Snowball Effect
- A Real World Example – Yearly Investment Contributions
- The Power of Starting to Invest Early in Life
- Making One Lump Sum Deposit and Letting it Ride at Different Rates and Years
- The Rule of 72
- Compound Interest with Debt
- Compound Interest Conclusion
- Compound Interest FAQs

**Compound Interest and the “Snowball Effect”**

The compounding effect of money is commonly referred to as a snowball effect. It starts slowly and it may seem like there’s no progress occurring because the gains and dividends barely trickle in. You definitely won’t get rich with compound interest at the beginning.

As time goes on, the money that you invested earns money.

Cool.

Years later, that new money earns money too.

All you have to do is put the money into an investment of your choice. Choosing a broad market ETF that tracks the S&P 500 or the S&P TSX 60 index is a good start.

Most people don’t apply this strategy to save and invest because they:

- Don’t save enough money.
- Didn’t learn about investing in school.
- Are too impatient to wait for the required time for compound interest to work.

Be patient and wait for the snowballing to happen. The earlier you get started, the longer the time horizon you give yourself. With a longer time horizon, you can earn sizeable sums of money even by doing a simple thing such as regularly purchasing an index ETF.

**How Simple Interest Works**

Before diving into compound interest, let’s take a step back and learn the basics of simple interest?

Simple interest is the money earned from the original money you deposited (the principal).

If you deposit $100 into your bank account and you earn 1% interest per year the principal is $100. The interest is $1 (1% multiplied by $100). At the end of the first year, you have $101 when combining your principal ($100) plus interest ($1).

Guaranteed Investment Certificates (GICs) often pay simple interest.

Suppose you had a three-year GIC where you receive interest annually and then you receive your principal and last interest payment at the end of year three.

The overall simple interest earned would be: **(principal x interest rate x amount of time**)

If you invested $1,000 at a 2% interest rate paid yearly for the three years, this would be the calculation:

Overall simple interest earned = ($1,000 x 2.00% x 3) = $60

The breakdown for each year would be:

Year 1: $1000 x 2.00% x 1 = $20

Year 2: $1000 x 2.00% x 1 = $20

Year 3: $1000 x 2.00% x 1 = $20

Total money back at the end of three years = Principal + interest payments which equals ($1000) + ($20+$20+$20) = $1,060.

You would receive $60 in interest and have your original $1,000 returned to you at the end of three years, for a total of $1,060 in your pocket.

**How Compound Interest Works**

Compound interest means you earn interest on the principal amount of money and on the interest previously earned as well. That’s where the difference lies. This one simple tweak in the equation makes an enormous difference.

Simple interest earns you money on the principal amount and that’s it. Compound interest earns you money on the principal amount **and all the interest that has been earned previously. **

Put another way, the interest you earn in year one gets added to the principal amount and then that new total amount earns interest in year two.

Year 1: $1000 x 2.00% x 1 = $20

Year 2: **$1020 **x 2.00% x 1 = $20.40

Year 3:** $1040.40** x 2.00% x 1 = $20.8

Total money back = Principal + interest payments, which equals ($1000) + ($20+$20.40+$20.81) = $1061.21.

You may look at the two scenario totals between simple and compound interest and wonder what the big deal is. Over three years, the difference in the totals was only $1.21.

Who cares?

Well, you should, because we haven’t revealed the magic.

**Comparison: Simple vs Compound Interest**

Below is a comparison of simple interest versus compound interest. In the simple interest scenario, you can see that no matter which investing year you are in, you are only earning $300 a year. Even as the total value of your investments goes up. In this scenario, imagine the interest rate is 6%.

The calculation for interest earned is equal to 6% multiplied by the original $5,000.

In a simple interest case, you only earn interest on the principal of $5,000. At the end of 10 years, you earn $3,000 ($300 per year x 10 years). Your total investment balance is worth $8,000.

Simple Interest $5,000 @ 6% | |||

Year | Jan 1 Investment Balance ($) | InterestEarned ($) | Dec 31 Investment Balance ($) |

1 | 5,000 | 300.00 | 5,300 |

2 | 5,300 | 300.00 | 5,600 |

3 | 5,600 | 300.00 | 5,900 |

4 | 5,900 | 300.00 | 6,200 |

5 | 6,200 | 300.00 | 6,500 |

6 | 6,500 | 300.00 | 6,800 |

7 | 6,800 | 300.00 | 7,100 |

8 | 7,100 | 300.00 | 7,400 |

9 | 7,400 | 300.00 | 7,700 |

10 | 7,700 | 300.00 | 8,000 |

Total Interest | $ 3,000.00 |

When you are earning compound interest, that means that you earn interest on the original money (the principal of $5,000) just like in the simple interest scenario, but you also earn interest on your interest previously earned.

Compound Interest $5,000 @ 6% | |||

Year | Jan 1 Investment Balance | InterestEarned | Dec 31Investment Balance |

1 | 5,000 | 300.00 | 5,300 |

2 | 5,300 | 318.00 | 5,618 |

3 | 5,618 | 337.08 | 5,955 |

4 | 5,955 | 357.30 | 6,312 |

5 | 6,312 | 378.74 | 6,691 |

6 | 6,691 | 401.47 | 7,093 |

7 | 7,093 | 425.56 | 7,518 |

8 | 7,518 | 451.09 | 7,969 |

9 | 7,969 | 478.15 | 8,447 |

10 | 8,447 | 506.84 | 8,954 |

Total Interest | 3,954.24 |

In Year 1, the amount of interest will be the same as in the simple interest example above. After the first year, the effects of compound interest can be seen more clearly. In Year 2 you can see that there is $318 of interest being earned in the compound interest scenario, which is more than the $300 that was earned in Year 2 of the simple interest example.

Remember, with compound interest, you earn interest on the principal amount and the interest you earned previously. So for Year 2, the interest is calculated on the amount of $5,300, which at 6% would earn you the $318. That $5,300 comprises the original $5,000 and the interest ($300) from year 1.

In Year 3, the opening balance is $5,618, with $5,000 coming from the principal and $618 representing the interest from years 1 and 2. In the third year, you would make roughly $337 in interest.

By the end of year 10, you earn $506.84 in compound interest which is significantly higher (68% higher) than the $300 you earn in Year 10 with only simple interest being calculated.

Overall, for the 10 years, you would earn $3,954 in compound interest versus $3,000 in simple interest. That’s an increase of almost 32%. As you can tell, compound interest can be very powerful.

**Factors that Affect Compound Interest**

Without turning this into a pure math lesson on the future value of numbers, there are factors that allow for the exponential growth of your money.

The factors are the principal amount, deposit amounts, frequency of deposits, the interest rate expected to be earned, and the amount of time you have to invest.

**Principal Amount.** This is the amount of money you invested originally. The more money you have initially, the better it is for you if you’re investing for the long term, all other things being equal. You can increase your principal amount by finding ways to save more money.

**Deposit Amounts.** This is the amount that you contribute throughout the years. If you deposit $100 per year your money will compound less than if you deposit $10,000 per annum.

**Deposit Frequency.** This is the number of times that you make investment deposits each year. If you make $100 contributions each month your money will compound faster than if you deposit $100 once per year.

**Interest rate.** The higher the interest rate or the rate of return on your investments is, the more money you will earn.

**Time**. This is a huge factor. The more years you have to let the money compound, assuming you’re invested in safer stocks or ETFs (keep in mind everything on the stock market carries a risk to some degree), the better it will be for you.

If you look at any large compound interest tables or graphs, you’ll notice that after 20 years, your investment portfolio rises a lot quicker than in the first 10-15 years.

Year | Jan 1 Investment Balance | Investment Earnings | Dec 31 Investment Balance |

1 | 5,000 | 300 | 5,300 |

2 | 5,300 | 318 | 5,618 |

3 | 5,618 | 337 | 5,955 |

4 | 5,955 | 357 | 6,312 |

5 | 6,312 | 379 | 6,691 |

6 | 6,691 | 401 | 7,093 |

7 | 7,093 | 426 | 7,518 |

8 | 7,518 | 451 | 7,969 |

9 | 7,969 | 478 | 8,447 |

10 | 8,447 | 507 | 8,954 |

11 | 8,954 | 537 | 9,491 |

12 | 9,491 | 569 | 10,061 |

13 | 10,061 | 604 | 10,665 |

14 | 10,665 | 640 | 11,305 |

15 | 11,305 | 678 | 11,983 |

16 | 11,983 | 719 | 12,702 |

17 | 12,702 | 762 | 13,464 |

18 | 13,464 | 808 | 14,272 |

19 | 14,272 | 856 | 15,128 |

20 | 15,128 | 908 | 16,036 |

21 | 16,036 | 962 | 16,998 |

22 | 16,998 | 1,020 | 18,018 |

23 | 18,018 | 1,081 | 19,099 |

24 | 19,099 | 1,146 | 20,245 |

25 | 20,245 | 1,215 | 21,459 |

26 | 21,459 | 1,288 | 22,747 |

27 | 22,747 | 1,365 | 24,112 |

28 | 24,112 | 1,447 | 25,558 |

29 | 25,558 | 1,534 | 27,092 |

30 | 27,092 | 1,626 | 28,717 |

*Interest compounded annually

Imagine you invest a one-time lump sum of $5,000 and your investment portfolio goes up by 6% on average. The table above shows the following total portfolio values at these year-end markers:

After 5 years: $6,691

After 10 years: $8,954

After 15 years: $11,983

After 20 years: $16,036

After 25 years: $21,549

After 30 years: $28,717

You can see that after fifteen years, your portfolio rose by about $7,000 to roughly $12,000 from the original $5,000 investment.

In the next fifteen years, your portfolio increased by another $17,000 (almost) to just shy of $29,000 overall.

Remember, you only invested the initial $5,000 and never added another dime. And your portfolio increased almost 6 times its original value in thirty years.

The table above shows the opening investment balance on January 1^{st} of each year. The third column shows the yearly interest received. You can see the dividend snowball effect taking place by looking at the yearly interest received.

You start in your first year earning $300 in interest, by the 13^{th} year that has doubled to $604 in interest earned for the year. After thirty years, you receive $1,626 in interest annually, or over five times your original yearly interest ($300). Simply astounding.

**The Compound Interest Snowball Effect**

Breaking down your interest earned into 5-year time intervals, you can see the exponential growth of the interest on a $5,000 initial investment that grows at 6% per year.

Timeframe | Interest Received in Time Period ($) | Percentage of Total Investment Gains |

Years 1-5 | 1,691 | 7% |

Years 6-10 | 2,263 | 10% |

Years 11-15 | 3,029 | 13% |

Years 16-20 | 4,053 | 17% |

Years 21-25 | 5,424 | 23% |

Years 26-30 | 7,258 | 31% |

Total | 23,717 | 100% |

Compound interest will not make you rich overnight, especially if you have small initial amounts. Even with $5,000 invested, only 7% of your total investment gains came from the first five years of your investment when looking at a 30-year investing period.

What you will notice is that almost a third (31%) of your total investment balance was earned in the last five years. More than half (54%) of your interest gains came from the last ten years. In other words, over half of your wealth was generated in the last 33% of the time.

Even more incredibly, the first 15 years of investing yielded you $6,983 in interest gains, but the last five years actually earned you more than that ($7,258). That is the power of compounding. Be patient because the returns are slow, but then they pick up speed.

In summary, you invested $5,000 over 30 years; it grew to a total balance of $28,717, meaning you now have an account that is worth 5.74 times the original amount.

Each dollar ($1.00) you invested 30 years ago grew to be $5.74 before taxes and inflation. You didn’t even add another cent of money. That is simply astounding.

**A Real World Example – Yearly Investment Contributions**

You may have noticed that in the previous simple example that $5,000 was deposited and then no additional investments were made. That doesn’t really happen in real life. You typically invest money each year.

Suppose you save $1,200 each year on January 1^{st}. Here is what would happen.

Compound Interest$5,000 @ 6% + $1,200 a year (beg. Year 2) | ||||

Year | Jan 1 Investment Balance | Investment Earnings | Dec 31Investment Balance | Running Total of Investment Gains |

1 | 5,000 | 300 | 5,300 | 300 |

2 | 6,500 | 390 | 6,890 | 690 |

3 | 8,090 | 485 | 8,575 | 1,175 |

4 | 9,775 | 587 | 10,362 | 1,762 |

5 | 11,562 | 694 | 12,256 | 2,456 |

6 | 13,456 | 807 | 14,263 | 3,263 |

7 | 15,463 | 928 | 16,391 | 4,191 |

8 | 17,591 | 1,055 | 18,646 | 5,246 |

9 | 19,846 | 1,191 | 21,037 | 6,437 |

10 | 22,237 | 1,334 | 23,571 | 7,771 |

11 | 24,771 | 1,486 | 26,257 | 9,257 |

12 | 27,457 | 1,647 | 29,105 | 10,905 |

13 | 30,305 | 1,818 | 32,123 | 12,723 |

14 | 33,323 | 1,999 | 35,323 | 14,723 |

15 | 36,523 | 2,191 | 38,714 | 16,914 |

16 | 39,914 | 2,395 | 42,309 | 19,309 |

17 | 43,509 | 2,611 | 46,119 | 21,919 |

18 | 47,319 | 2,839 | 50,158 | 24,758 |

19 | 51,358 | 3,082 | 54,440 | 27,840 |

20 | 55,640 | 3,338 | 58,978 | 31,178 |

21 | 60,178 | 3,611 | 63,789 | 34,789 |

22 | 64,989 | 3,899 | 68,888 | 38,688 |

23 | 70,088 | 4,205 | 74,294 | 42,894 |

24 | 75,494 | 4,530 | 80,023 | 47,423 |

25 | 81,223 | 4,873 | 86,097 | 52,297 |

26 | 87,297 | 5,238 | 92,535 | 57,535 |

27 | 93,735 | 5,624 | 99,359 | 63,159 |

28 | 100,559 | 6,034 | 106,592 | 69,192 |

29 | 107,792 | 6,468 | 114,260 | 75,660 |

30 | 115,460 | 6,928 | 122,387 | 82,587 |

Overall, you invested $5,000 (your first year) and then made $34,800 ($1,200 * 29 years) of lump-sum payments for a total of $39,800 in contributions.

In the previous scenario, you only invested $5,000 one time and let it grow at 6% yearly for 30 years. You ended up with a final investment balance of $28,717.

By contributing an extra $1,200 each year over the next 29 years, your final investment balance in this current scenario rocketed from $28,717 to $122,387.

You contributed $34,800 more over that timeframe than the previous example, yet your final investment balance was $93,670 higher thanks to compound interest.

You have now learned the importance of investing and leaving your money untouched for a long time. You have also seen how you can supercharge your investment totals by saving money and contributing every year to your investments.

**The Power of Starting to Invest Early in Life**

Now you will learn why it is important to invest early and often.

Imagine you save $2,400 and invest it on January 1st when you are 25 years old.

You continue depositing $2,400 at the beginning of each year for 14 more years for a grand total of $36,000 in contributions. You make no further investments.

If your account continues to grow by 6% per year, you would end up with $269,387 by the time you are 65 years old.

Your friend Oscar spent oodles of money from the time he graduated from university. He finally started saving for retirement at the age of thirty-five. He deposits $2,400 into his account at that time, but he started one decade later than you. Will it make a difference?

Oscar contributes the same $2,400 per year, but he does it for 30 years instead of the 15 years you did because he realizes he needs to play “catch up”. Oscar ends up making $72,000 in contributions, which is twice the amount that you did.

How much will Oscar end up with at 65?

$213,191 if he earns the same 6% per year.

This is $56,196 less than you and you only contributed half the amount he did. The other difference between you and Oscar was that you started investing a decade earlier. That shows the power of starting earlier in life and having time on your side.

Just to drive the point home, even more, your other friend Priya invested $6,000 into her brokerage account when she was 25 and made the same lump sum payment for four more years.

Over a five-year span, Priya deposited $30,000 into her account. After her thirtieth birthday, she didn’t invest another dime.

Priya would end up with $292,095 in her investment account if the average rate of return was 6% per year.

Name | Contribution Per Year ($) | Years Adding Funds | Total Contributions ($) | Age of Contributions | Final Investment Balance ($) |

You | 2400 | 15 | 36000 | 25-40 | 269,387 |

Oscar | 2400 | 30 | 72000 | 35-65 | 213,191 |

Priya | 6000 | 5 | 30000 | 25-30 | 292,095 |

Priya contributed only $30,000 in this scenario, which is $6,000 less than you did. The difference was she invested larger amounts earlier in life and allowed it to compound the interest for more time.

Invest early. Invest often. Then sit back and watch time and compound interest do the magic.

**Making One Lump Sum Deposit and Letting it Ride at Different Rates and Years**

Here is a table that you can use as a quick reference guide to see how an investment of $10,000 deposited at different interest rates would fare at the time intervals of 1, 5, 10, 15, 20, 25 and 30 years.

For example, if you deposited $10,000 at 2% then after 15 years you would have $13,459 in your account. If you deposited $10,000 at 6% for 25 years, you would have $42,919.

A higher return rate earned on your investments means your total balance will grow more. As you give your investments more time to grow, your balance will get higher and higher.

$10,000 Invested | Interest Rate | |||||||||

Years | 1% | 2% | 3% | 4% | 5% | 6% | 7% | 8% | 9% | 10% |

1 | 10,100 | 10,200 | 10,300 | 10,400 | 10,500 | 10,600 | 10,700 | 10,800 | 10,900 | 11,000 |

5 | 10,510 | 11,041 | 11,593 | 12,167 | 12,763 | 13,382 | 14,026 | 14,693 | 15,386 | 16,105 |

10 | 11,046 | 12,190 | 13,439 | 14,802 | 16,289 | 17,908 | 19,672 | 21,589 | 23,674 | 25,937 |

15 | 11,610 | 13,459 | 15,580 | 18,009 | 20,789 | 23,966 | 27,590 | 31,722 | 36,425 | 41,772 |

20 | 12,202 | 14,859 | 18,061 | 21,911 | 26,533 | 32,071 | 38,697 | 46,610 | 56,044 | 67,275 |

25 | 12,824 | 16,406 | 20,938 | 26,658 | 33,864 | 42,919 | 54,274 | 68,485 | 86,231 | 108,347 |

30 | 13,478 | 18,114 | 24,273 | 32,434 | 43,219 | 57,435 | 76,123 | 100,627 | 132,677 | 174,494 |

#### $2,400 Invested Per Year at the Beginning of the Year – Example

Here is a more realistic example where you put in $2,400 at the beginning of each year into your investment account. Below is a table of final investment balances at different interest rates earned and different durations for the investment period.

You start with $0 in your account, so in the first year on January 1^{st} you decide to lump sum invest $2,400.

Keep in mind that after one year you would have contributed $2,400, $12,000 after 5 years and $24,000 after ten years. After 20 years, you would have contributed $48,000 and after 30 years, you would have deposited $72,000 into this investment account.

What you will notice is that by investing the equivalent of $200 a month for 30 years, and earning a 7% return on your investments (which – it should be noted – you don’t have control over), you would end up with almost a quarter million of a dollars, at $242,575.

Can you save $200 a month, or $2,400 a year? It could be life changing. Think about that the next time you’re hitting the club. Maybe don’t buy a round of drinks. You don’t need bottle service, do you?

Interest Rate | ||||||||||

Years | 1% | 2% | 3% | 4% | 5% | 6% | 7% | 8% | 9% | 10% |

1 | 2,424 | 2,448 | 2,472 | 2,496 | 2,520 | 2,544 | 2,568 | 2,592 | 2,616 | 2,640 |

5 | 12,365 | 12,739 | 13,124 | 13,519 | 13,925 | 14,341 | 14,768 | 15,206 | 15,656 | 16,117 |

10 | 25,360 | 26,805 | 28,339 | 29,967 | 31,696 | 33,532 | 35,481 | 37,549 | 39,745 | 42,075 |

15 | 39,019 | 42,334 | 45,977 | 49,979 | 54,378 | 59,214 | 64,531 | 70,378 | 76,808 | 83,879 |

20 | 53,374 | 59,480 | 66,424 | 74,326 | 83,326 | 93,583 | 105,276 | 118,615 | 133,835 | 151,206 |

25 | 68,462 | 78,410 | 90,127 | 103,948 | 120,272 | 139,575 | 162,424 | 189,491 | 221,578 | 259,636 |

30 | 84,319 | 99,311 | 117,606 | 139,988 | 167,426 | 201,124 | 242,575 | 293,630 | 356,581 | 434,264 |

**The Rule of 72**

The Rule of 72 states that if you divided the number 72 by your expected rate of investment return, then the answer is will tell you how long (in years) it would take your money to double.

So if you were expecting your investments to earn 6% per year, then it would take 72/6 = 12 years to double your original money.

For instance, if you invested $100,000 and expected to earn 6% a year on your investments, then your investment portfolio would be worth $200,000 (or double the $100,000 value) 12 years from now.

**Compound Interest with Debt**

You saw how awe-inspiring compound interest was when it was earning you money. However, there is a dark side to compound interest, and that’s when you are dealing with debt.

Most of the examples above were dealing with an interest rate of 6%. For credit cards, your interest rate is 20% if you don’t pay back the full monthly balance.

If you cannot pay off your credit card balance and the debt keeps piling up, it won’t take long for it to become a debt mountain. This is not something you want to deal with.

Avoid credit card debt as much as possible. Don’t invest until you have tackled most of your consumer debt because the interest rates can be astronomical.

## Compound Interest Conclusion

Now that you know how compound interest works, it’s time for you to start saving money and investing it. The earlier you start, the better off you will be.

Have you experienced the magic of compound interest yet?

## Compound Interest FAQs

**Can you get rich from compound interest?**

If you have a long time horizon (decades) and the discipline and temperament to weather the rough times the stock market will throw at you, then yes you can build wealth from compound interest.

Compound interest is magical because once you begin investing you earn interest, over time, your interest begins earning its own interest. If you invest $500 per month ($6,000 annually) and earn 7% for 30 years, you will have a shade less than $610,000, of which you only contributed $180,000. The other $430,000 is due to compound interest.

**How do you become a millionaire with compound interest?**

If you invest $820 per month and earn 7% per year, then over 30 years you will reach $1,000,000.

If you have a longer timeframe, such as 35 years, then you only need to invest around $560 per month at 7% interest to become a millionaire.

Compound interest becomes more powerful as you give it more time to work.

**What is the Rule of 72 and compound interest?**

The Rule of 72 determines how long it takes you to double your investment based on the interest rate you will earn.

You divide 72 by your rate of return to get an answer which is the amount of time in years it will take to double your money.

If an investment will yield a 6% return then you divide 72 by 6 and get an answer of 12 years. That means your investment will double in 12 years.

Related Articles

Here are some important investing articles to check out.

- Learn all about risk tolerance (blog post)
- Compare ETFs, index funds and mutual funds (blog post)
- Discover all you about investing in your TFSA (blog post)
- Understand more the RRSP account (blog post)
- Discover all the common asset classes in investing (blog post)