What is compound interest, and why bother with it? Compound interest investment is a powerful tool and even a \$1 investment is worth a whole lot more later on.

It might seem easier to make a larger, riskier decision right off the bat, but in truth, compound interest is perhaps the most powerful tool in your investment arsenal. Albert Einstein once called it the most important invention in all of human history. So why do so few of us take advantage? Most people simply don’t take the time to fully understand the concept.

But you’re not one of those people. You want to fully understand the definition of compound interest and how it works so that you can mindfully save. Here’s how a compound interest investment puts time on your side and leads to you to financial freedom, one dollar at a time.

## What is the Interest Rate Definition?

In finance, interest rate is defined as the amount charged by a lender to a borrower for the use of an asset. So, for the borrower the interest rate is the cost of the debt, while for the lender it is the rate of return.

Note that in the case where you deposit into a bank (e.g., put money in your savings account), you have, from a financial perspective, lent money to the bank. In such a case the interest rate reflects your profit.

## How does Compound Interest differ?

Compound interest is defined as interest that is earned not solely on the initial amount invested but also on any further interest. In other words, compound interest is the interest of both the initial principal and the interest that has been accumulated on this principle so far. This concept of adding a carrying charge makes a deposit or loan grow at a faster rate.

You can use the compound interest equation to find the value of an investment after a specified period or to estimate the rate you have earned when buying and selling some investments. It also allows you to answer some other questions such as how long it will take to double your investment.

## OK, let’s talk about compound interest versus simple interest

The \$1,000 Mitch originally invested grew through compounding interest. In other words, the fund’s gains were reinvested. Interest grew on top of the principal and the reinvested gains. Compound interest is the magic force that stimulates the wild proliferation of an investment when it’s left alone for long enough. As time goes on, interest leads to more money, over and over again. This is a good thing.

But it’s worth noting that not all investments use compound interest. Many bond and stock investments use simple interest so earnings are simply paid out, not reinvested. Simple interest is great when you’re borrowing money like to pay for a car or home, but it’s decidedly suboptimal when you’re trying to grow investments. But two common places where you will compound your gains: savings accounts and dividend reinvestment in your portfolio.

Here is the key question to ask when assessing the potential of any investment: Is the money that accrues from dividends being reinvested to be factored into future returns calculations? If yes, you can breathe easier. You’ll benefit from the impact of compounding.

## The Compound Interest Formula

The compound interest formula is an equation that lets you estimate how much you will earn with your savings account. It's quite complex because it takes into consideration not only the annual interest rate and the number of years but also the number of times the interest is compounded per year.

The formula for annual compound interest is as follows:

FV = P (1+ r/m)^mt

Where:

FV - the future value of the investment, in our calculator it is the final balance
P - the initial balance (the value of the investment)
r - the annual interest rate (in decimal)
m - the number of times the interest is compounded per year (compounding frequency)
t - the numbers of years the money is invested for

It is worth knowing that when the compounding period is one (m = 1) then the interest rate (r) is called the CAGR (compound annual growth rate).

## Example of Compound Interest

The first example is the simplest, in which we calculate the future value of an initial investment.

### Question

You invest \$10,000 for 10 years at the annual interest rate of 5%. The interest rate is compounded yearly. What will be the value of your investment after 10 years?

### Solution

Firstly let’s determine what values are given, and what we need to find. We know that you are going to invest `\$10,000` - this is your initial balance `P`, and the number of years you are going to invest money is `10`. Moreover, the interest rate `r` is equal to `5%`, and the interest is compounded on a yearly basis, so the `m` in the compound interest formula is equal to `1`.

We want to calculate the amount of money you will receive from this investment, that is, we want to find the future value `FV` of your investment.

To count it, we need to plug in the appropriate numbers into the compound interest formula:

`FV = 10,000 * (1 + 0.05/1) ^ (10*1) = 10,000 * 1.628895 = 16,288.95`

The value of your investment after 10 years will be \$16,288.95.

Your profit will be `FV - P;` It is `\$16,288.95 - \$10,000.00 = \$6,288.95`.

## But you have to leave your investment alone. This is important.

The wonderful thing about compounding is how it creates new money in a way that shakes the laws of physics. The downside? For it to pay off, you have to take a hard “hurry up and wait” strategy to managing your investment. This can be comforting to some (“You mean I have to mostly just do nothing? Uh, yeah, I’ll take two, thanks.”) but seriously challenging to a lot of people.

If you’re struggling with the idea of doing nothing, here’s a framework to estimate how long your suffering (your very, very financially advantageous suffering) might last. To calculate how quickly your investment doubles with the impact of compounding, use the “Rule of 72.” Take the number 72 and divide it by the percent annual return. The result is the number of years it will take for your investment to double, assuming you don’t make any additional investment. For example, an investment with a rate of return of 6% will double in 12 years; a rate of return of 8% will double in nine years. When rates of return is compounded more than once a year, your money doubles even faster. In comparison, simple interest would still theoretically double your money – eventually.

As you’ve probably figured out, the biggest factor in growing your money with compound interest is, in fact, time. Compound interest and time are the sunlight and water of growing your money.

Let’s say, for example, that you want to have \$1 million by the time you reach age 65. Here’s how much you would have to save each month, depending on the age you start: As with most things, like skincare and sleeping more, the earlier you start investing, the better. If you get in the long game by age 25, you’re truly killing it. All is not lost if you don’t start investing until after that, but the pressure is on to save more the longer you wait to get started.

## Key Takeaways

• Invest early – As with any investment, the earlier one starts investing, the better. Compounding further benefits investors by earning money on interest earned.
• Invest often – Those who invest what they can, when they can, will have higher returns. For example, investing every month instead of every quarter results in more interest.
• Hold as long as possible – The longer you hold an investment, the more time compound interest has to earn interest on interest.
• Consider interest rates – When choosing an investment, interest rates matter. The higher the annual interest rate, the better the return.
• Don't forget compounding intervals – The more frequent investments are compounded, the higher the interest accrued. It is important to keep this in mind when choosing between investment products.