One of the easiest ways to understand how interest works is to think of the interest you earn as the speed at which your money grows. If you choose to keep your savings stashed away under a loose floorboard in your house, itâ€™s like a car thatâ€™s parked, and your speed is zero miles per hour. When you consider the effect of inflation, the car is rolling backwards slowly. Inflation, itself, is a type of compound interest â€“ but applied to the cost of living. Youâ€™ll want your savings or earnings to outpace inflationâ€™s compounding.

If you put your savings into an investment that pays simple interest, the car is moving ahead â€“ but thereâ€™s a low speed limit. The speed limit is the interest rate, but speed is also governed by how often the interest is applied. Given enough time, you might reach your destination eventually, but it will be a slow ride. Simple interest means that you earn a fixed amount of interest on a deposit, but that the interest is only applied to the principal. If you earn 5% interest on a $100 deposit with simple interest, youâ€™ll earn $5 on that deposit every year. Your money is growing, but slowly.

By comparison, compound interest is like putting rocket fuel in your car â€“ although, at first, it looks a lot like simple interest. Depositing the same $100 into an account that pays 5% compound interest produces results that arenâ€™t very impressive when you begin saving. In the first year, your compound interest account will look almost exactly like a simple interest account. But youâ€™ll notice the balance is just a bit higher if you compare the two. The difference occurs because the interest youâ€™ve earned is generating interest of its own.

By year two, youâ€™ll start to see a bigger difference between a simple interest account and a compound interest account. If you plot the account growth on a chart, the simple interest account will be a straight line with a slight incline. The compound interest line will begin to curve upward, becoming steeper and steeper as time passes.

Itâ€™s helpful to understand when simple interest is used and when compound interest is used in the real world. Certificates of Deposit (CDs) are a great real-world example of an account that pays simple interest, although not all CDs use simple interest. Letâ€™s assume this one does. If you deposit $1,000 into a 12-month CD that pays simple interest, youâ€™ll earn 5% interest. If you close the CD at maturity, youâ€™ll have $1,050, which is your initial deposit of $1,000 plus $50 youâ€™ve earned in interest.

If you took the same $1,000 and instead deposited the money in a savings account that pays 5% compound interest, at the end of the year, youâ€™ll have $1,051.16. Your original deposit, the principal, is $1,000 and youâ€™ve earned $51.16 in interest. Earlier, we pointed out that the difference between simple interest and compound interest would be small at first. In this example, the difference is one dollar and change.

The difference, while small at first, is due to compounding. In this case, the savings account compounds interest monthly. Rather than applying a 5% return at the end of the year, like with the CD, the bank is paying you 0.4166% monthly, which is 5% divided by 12. By month two, your interest is earning interest as well. The results arenâ€™t too impressive at first, but over a longer time period, magical things happen.

Letâ€™s look at the difference when we use longer time frames.

Year | Simple interest earned | Compound interest earned | Difference |

1 | $50 | $51.16 | $1.16 |

5 | $250 ($50×5) | $283.36 | $33.36 |

10 | $500 ($50×10 | $647.01 | $147.01 |

20 | $1,000 ($50×20) | $1712.64 | $712.64 |

30 | $1,500 ($50×30) | $3,467.74 | $2,467.74 |

40 | $2,000 ($50×40) | $6,358.42 | $5,358.42 |

After 40 years, your simple interest earnings have tripled your money. Your $1,000 deposit is now worth $3,000. However, with compound interest, your $1,000 has become $7,358. Youâ€™ve earned over $6,300 on your initial deposit of $1,000.

There are four primary components to consider when understanding simple interest and compound interest.

- Principal: The principal is the base to which the interest is applied. In the earlier examples, the principal is the money youâ€™ve deposited. Principal can also be an amount borrowed, to which interest is also applied.
- Interest rate: The interest rate is the percentage that will be applied to the principal. An interest rate is a broad term that doesnâ€™t always make clear â€“ by itself â€“ how the interest is compounded. While expressed as an annual figure, called an annual percentage rate (APR), interest might be compounded annually, monthly, weekly, daily, or at other intervals.
- Compounding frequency: This refers to how often the interest is applied. An annual interest rate may be compounded monthly or at other periodic intervals, creating whatâ€™s called an annual percentage yield (APY).
- Length of investment: Time is your friend with compound interest â€“ at least when it comes to earnings. If compound interest is applied to a debt, the debt can become costlier over time.

Making additional deposits can also have an enormous effect on compounding, although the math doesnâ€™t change; youâ€™re simply putting more money to work where it can earn interest and its interest earnings can earn interest as well.

While the difference in earnings in our earlier examples is small after a year, the amount of the principal, the interest rate, the compounding frequency, and the length of your investment all play a role in how quickly your money can grow when measured in dollars.

## Compounding and investments

Compounding is a powerful tool for increasing earnings, as we saw in the earlier examples that involved savings. But compounding is also how many of todayâ€™s millionaires and billionaires built their nest eggs.

A savings account or similar type of account is useful for building an emergency fund or for saving toward a short-term goal. When saving for a secure future, youâ€™ll want a little more octane in your fuel, meaning a higher rate of return. Currently, most savings accounts or similar types of accounts pay 2% APR or less. Even with a large balance, your earnings may not be large enough to fund your retirement years. This is why most 401(k)s and IRAs are focused on stocks or mutual funds, which in turn purchase stocks.

Youâ€™ve seen it on the news: headlines about stocks soaring â€“ or taking a plunge. To many, stocks seem like risky business. In truth, stocks can be quite risky. More accurately, buying individual or tightly-related groups of stocks is risky. Investors who were heavily invested in tech stocks lost massive amounts of money when the Dotcom tech bubble burst in 2000. Many owners of real estate investment trusts, or REITs, are still underwater on their investments after the housing bubble burst in 2008.

There are safer ways to invest, however, bringing strong returns over time with less risk of losing it all. The good news is that you donâ€™t have to guess where to invest. Instead, let history be your guide.

For example, since its inception in 1928, the S&P 500 has had an average annual return of about 10%. To be fair, some years the index is up and some years it is down. Weâ€™re looking at averages and trying to broaden the time frame to ensure the averages are more likely to hold true. In a way, the S&P 500 is a cross section of the 500 biggest companies that define the American economy, an index of 500 stocks that lead in many diverse industries. If tech companies are on the ropes one year, companies that focus on household goods or pharmaceuticals might carry the index and keep returns strong. With exposure to so many companies, the index reduces risk by limiting exposure to any one sector.

The S&P isnâ€™t the only index. Youâ€™ve likely heard of the Dow Jones Industrial Average, or DJIA. This famous index is made of 30 large stocks traded on the New York Stock Exchange. While the industries in the Dow are also diverse, the index is less diverse then the S&P 500, as well as having fewer stocks.

Investing in index funds is easier than ever. These funds effectively track an index, like the S&P 500, going up when the index goes up and going down when the index goes down. Interestingly, index investing, if you pick a broad index, is one of the most successful ways of investing while also being among the easiest ways to invest. Broad market index funds historically outperform most funds run by managers who hand-pick stocks.

Letâ€™s apply compounding to index investing.

In this example, you just turned 20. Youâ€™ve got a part-time job and youâ€™re in college. Many of your expenses are covered and you have some extra money you can invest. Look into a Roth IRA for this venture. If you use a Roth, in most cases, the funds are tax-free when you withdraw â€“ but youâ€™ll be investing after-tax funds.

Letâ€™s also assume that you choose to use an index fund to build your IRA. You have $50 per week in uncommitted funds that you can invest, which still leaves you enough to build your emergency savings and split a pizza with your friends every now and then.

Youâ€™ve researched the S&P and youâ€™ve learned that the average rate of return is about 10% for the index. The investment should grow significantly over time, assuming you can keep up the pace of contributing $50 per week.

The investment account has a $500 minimum requirement to open the account and avoid fees. Your $50 per week investment comes out to $212.50 each month, because there are 4.25 weeks in a month, which is $2,550 per year.

Assuming an average rate of return of 10%, about the same as the historical rate, hereâ€™s what the numbers might look like:

After 1 year: Youâ€™ve contributed $3,050 and your account is worth $3,100. While the $50 gain isnâ€™t much, youâ€™ve only been investing for a year.

After 10 years: Youâ€™ve contributed $26,000 and your account is worth nearly $42,000. Youâ€™ve earned $16,000 by just leaving the money there to grow and by staying consistent in your investing.

After 20 years: Now, youâ€™ve invested $51,500 and your account balance is nearly $150,000. Youâ€™ve earned almost $100,000 by investing consistently â€“ without a need to be a genius stock picker. You just invested in the S&P 500 index and let time take care of the growth.

After 30 years: Your total investment is $77,000 but your account is now worth $428,000.

After 40 years: Congratulations, youâ€™re a tax-free millionaire. Youâ€™ve invested $102,000 but now your account is worth over $1,150,000 â€“ and because you invested using a Roth IRA, you can withdraw the money tax free when you reach retirement age.

The account value would reach nearly $1.9 million by the time you are 65 and have been investing steadily for 45 years.

## The rule of 72

If youâ€™re interested in knowing how long it will take to double your money using compound interest, the rule of 72 is simple and useful formula you can use for estimates.

All you need to do is divide 72 by the interest rate to estimate how long it will take to double your money.

72 / <interest rate> = years to double

For example, if you invest in a fund that has an average annual return of 7%, your money will double in just over 10 years.

72 / 10 = 10.28

The precise formula is more complex, but the rule of 72 is easy to remember and provides a reasonably close estimate when considering investments.

## Interest rates for credit

Weâ€™ve seen how compound interest affects savings accounts or investments. Compound interest can also come into play with credit.

Many types of credit utilize simple interest, which works to your advantage. However, because interest is usually applied to the outstanding balance, interest is particularly expensive at the beginning of a loan, even with simple interest applied.

One notable exception is credit cards, which do charge compound interest. If you have a high interest rate credit card, youâ€™re more likely to feel the effects of compound interest as new interest is added to your balance and more interest is then charged on the higher balance that includes old interest.

Of all the types of debt, credit card debt is often the most expensive and the most difficult to escape. Compound interest is a big part of what makes credit card debt so difficult to pay off. Wherever possible, funnel extra money toward any credit card debt you may have which will reduce your interest costs.