If you’d like to amass wealth and live comfortably, few things are as important as compound interest.

In finance, compound interest refers to the effect of earning ‘interest on interest’.

It helps to explain why investing money over a long term horizon is extremely powerful due to the fact that your wealth can grow more quickly from earning money on the earned money.

The bar chart below shows how the starting account balance quickly grows due to earning interest and accelerates when the interest starts to earn interest.

## How Does Compound Interest Work?

We already learned that compound interest refers to the effect of earning ‘interest on interest’. But what does that mean in practice?

First, to compound something means to augment it or intensify it.

At a basic level, you need to understand that the more money you save and invest, the more you will gain in investment returns and interest. As your money grows, it will compound, or augment. The new growth will be based on a higher balance, which will mean you will passively gain more dollars every year.

To make it easy to understand, let’s start with a very simplified example. Assume that you won a contest and the prize is one dollar. That’s $1.00. However, each morning for 30 days you are entitled to present each dollar and exchange it for two dollars. So on day two, you will have $2, on day three you will have $4, on day four you’ll have $8. By day fifteen you will have $16,384. And finally on day 30 you will have $536,870,912!

What happened between day 15 and day 30 to cause the sum from going from a respectable $16,384 to over half a billion dollars? The answer is compound interest.

As your balance grows, the effect of doubling your money gets even larger!

## Compound Interest Formula

In order to calculate the final value of a sum of money after a specific amount of time, there’s a formula that you can use.

FV = P (1+r/n)^nt

FV = future value

P = initial principal balance

r = interest rate

n = number of times interest compounds per time period

t = number of time periods

Therefore, if someone asks you how much money they would owe have from an investment after 5 years if they started with a balance of $1,000 and the return was a rate of 14% compounded monthly (12 times per year), you could plug the assumptions into the formula to figure it out.

P = $1,000

r = 14%

n = 12

t = 5

FV = $1,000 [1+(0.14/12)]^5×12 = $2,005.61

The formula doesn’t necessarily only apply to investments either.

For example, you could use this formula to answer if someone asks you how much money they would owe on their credit card after 5 years if they started with a balance of $1,000 and the interest rate was 14% compounded monthly (12 times per year).

## Another Illustrative Compound Interest Example

For this next, and more realistic example, we have two people. Letâ€™s call them â€˜Sam the Spenderâ€™ and â€˜Sue the Saverâ€™. Even though both have the same job and live together, â€˜Sam the Spenderâ€™ only has $6,000 in the bank. â€˜Sue the Saverâ€™ on the other hand, has $11,000 in the bank.

Letâ€™s assume that they donâ€™t save any additional money, so they only contribute what they currently have. Remember that â€˜Sam the Spenderâ€™ has $6,000 and â€˜Sue the Saverâ€™ has $11,000.

They are able to invest their money in stocks at an annual return of 5%. Letâ€™s see what would happen if they forget about the money and donâ€™t touch if for 10 years.

Initially, â€˜Sam the Spenderâ€™ has $5,000 LESS than â€˜Sue the Saverâ€™. Since they didnâ€™t add any additional money to their account, and both earn 5% annually, it would seem logical that after 10 years, â€˜Sam the Spenderâ€™ would still have $5,000 less than â€˜Sue the Saverâ€™.

**But thatâ€™s not what happens.**

By the end of 10 years, â€˜Sam the Spenderâ€™ has $7,757 FEWER dollars than â€˜Sue the Saverâ€™.

How can this be?

Compound interest!

## The Power Of Compound Interest

What compound interest does, is base the new annual growth number on the larger balance. So 5% of a larger number will mean a larger amount of dollars are being added in investment growth.

We all understand that if a million dollars grows by 5%, the difference in dollars will be larger than if $10,000 grows by 5%.

This effect is further amplified if you save and invest additional dollars over time. Youâ€™ll be getting the double effect of your savings being added to the balance and the growth of your investments.

This seems rather simple and straightforward though, right? So why are we spending the time to show you this example?

## Why Does Compound Interest Matter?

Compound interest matters because itâ€™s one of the core principles to building wealth. Most people understand, at a basic level, that if they have more money they will make more money.

Yet lifestyle creep, lifestyle inflation, or the desire to keep up with the Joneses still leads people to spend on things they donâ€™t need.

If you really sit down and understand how much a dollar today will be worth in 20 years, you may think twice before buying that extra thing you donâ€™t need.

In our example above, a dollar today will be worth $1.55 at the end of the 10 year period. That means that $500 phone will actually cost you $775. Things will end up costing you a lot more than the sticker price once you realize the missed opportunity to invest and grow your money.

And no, we donâ€™t think you should go and try to save every single penny and cheap out on everything. But if learning how to spend mindfully and use your money intentionally can help you be happier and save more. Itâ€™s a win-win.

After all, research shows that all of those physical products wonâ€™t bring you sustained long-term happiness.

In the clip below, you can see NFL player Carl Nassib explaining the power of compound interest to his teammates on the Cleveland Browns. Check it out!

## FAQs

**What is the compound interest formula?**

FV = P (1+r/n)^nt

FV = future value

P = initial principal balance

r = interest rate

n = number of times interest compounds per time period

t = number of time periods

**What Is Compound Interest**

The effect of earning ‘interest on interest’.

Camilo is a personal finance expert and the Co-Founder and CEO of The Finance Twins. I was raised in poverty by a single mother and had to learn everything about personal finance on my own. I have been featured on Forbes, Business Insider, CNBC, and US News. Earlier in my career, I worked as an investment banking analyst on Wall Street at JPMorgan Chase & Co., and I have an M.B.A. from Harvard University and a B.S.E. in finance from the Wharton School of the University of Pennsylvania.