# Compound Interest: The Magical Power of Compounding

Compound interest (or compounding interest) is a concept that is simple to understand but its incredible, almost magical power is not obvious to everyone. This article will explain how compound interest works and demonstrate why the amount of time you stay invested is as important as the amount of invested money.

## What is Compound Interest?

In simple terms, compound interest is the interest earned on interest or the earnings on your earnings.

## How Does Compound Interest Work?

Let's base this example on a hundred dollars to make the calculations easier. If you invest $100 at an annual interest rate of 5%, you will have $105 by the end of the first year. At the end of the second year, you will have $110.25. You will earn another $5 on the initial $100 deposit and $0.25 on the previously earned interest of $5.

Twenty five cents doesn't sound like much, but this is just the beginning. At the end of the third year, you will have $115.76. This amount will be comprised of the initial $100 deposit that earned $5 for the year and your previously accumulated interest of $10.25 that also earned $0.51. The year after, the interest on your interest will earn you an additional $0.79. The earnings on your earnings will continue to accelerate each year, and the more time your money has to grow - the greater the effect of compounding will be. Like a rapidly growing snowball that is rolling down a snow-covered hill.

If you keep your $100 for your retirement without ever adding more money, in 30 years you will end up with $432.19. Let's break down this amount as well. In 30 years your $100 earned you only $150 in simple interest, meaning the interest earned purely on the initial amount at an annual interest rate of 5%. But the compounded interest or the earnings on your earnings got you an additional $182.19. Yes, the interest earned on interest brought in more money than your initial amount. And that is the power of compounding.

Let's continue making it more exciting by raising the stakes.

## Compound Interest Results Over Time

Let's see how much your wealth can multiply over time thanks to the power of compounding. The table below shows the effect of time and different rates of return for the initial investment of $10,000.

## Compound Interest Chart

Duration | 4% | 8% | 10% | 12% |
---|---|---|---|---|

10 Years | $14,802 | $21,589 | $25,937 | $31,058 |

20 Years | $21,911 | $46,610 | $67,275 | $96,463 |

30 Years | $32,434 | $100,627 | $174,494 | $299,599 |

40 Years | $48,010 | $217,245 | $452,592 | $930,510 |

50 Years | $71,067 | $469,016 | $1,173,908 | $2,890,022 |

If a 20-year-old invests a lump sum of $10,000 today in a low-risk investment that yields 4% annual interest for the next 50 years, they will have $71,067 in their retirement savings. If they had invested in a more aggressive asset allocation mix, that mainly consisted of stocks, earning a 10% annual return over the same time, they would end up with $1,173,908. Designing an investment portfolio with an average annual rate of return of 12%, just 2% higher, will earn them $2,890,022. If the investments were held in a tax-free account such as a Roth IRA, all future withdrawals will be tax-free.

## Compounding Periods

When we talk about interest being compounded - we mean that the interest is accrued and added to the principal amount of the previously compounded amount. The interest can be compounded at different time intervals - daily, monthly, quarterly, annually, or at any other intervals. If the interest on an investment or a deposit is compounded annually - it means that the interest is credited to the principal amount every year.

The number of compounding periods makes a significant difference - the higher the number of compounding periods, the greater the amount of compound interest. That is because the interest is added more often to the total amount and it starts earning interest on itself as soon as it is credited.

## Compound Interest Can Work Against You

Compound interest is the eighth wonder of the world. He, who understands it, earns it; he who doesn't, pays it. This quote attributed to Albert Einstein is often used in personal finance articles. We tried to verify the quote by finding its source but couldn't find any significant evidence that Einstein said anything similar to this. We also think that it's unlikely that Einstein would say that. Nevertheless, although a bit corny, it's a good quote. It teaches us two things - one should never trust citations from unverified sources and that the power of compounding can work against you as well.

If we reverse the previous examples we can see how much money can flow in opposite direction and how compound interest will work against you when you borrow. In the United States, mortgages and car loans, for example, use simple interest, meaning it's not compounded. But credit card interest is typically compounded daily, based on the average daily balance.

Let's review another example that shows how much credit card companies can make off of you. If you constantly carry an average credit card balance of $5,000 with a 22% annual interest rate for the next 10 years - you will have to pay $40,095 in interest. Forty thousand ninety-five dollars. That is 3.6 times more than $11000 in simple annual interest or an additional $29,095 of interest on interest earnings.

People who carry credit card balances from month to month are continuously racking up interest charges and own interest on the money that they technically didn't borrow. The outstanding credit card balances compound every day and grow rapidly, leading many people into a debt trap. Compound interest can be one of the biggest stumbling blocks to becoming debt free. For some people who carry credit card balances or loans with compound interest, paying off their debt can be the best thing they can do for their financial future.

## How to Calculate Compound Interest?

Use this online compound interest calculator to determine how much your money can grow with the power of compound interest. You can also calculate compound interest by using the formula below or quickly estimate how long it will take for your money to double by using the Rule of 72.

### Rule of 72

The Rule of 72 is a quick way to estimate how your investments will grow over time. Divide 72 by the expected rate of return or interest rate and you will get the approximate number of years it takes to double your money. For example, if your expected rate of return is 10%, divide 72 by 10, and the result is your investment will double every 7.2 years (72 / 10% = 7.2).

## Compound Interest Formula

Use this formula to calculate the amount of compound interest of $10,000 deposit at an interest rate of 4% that compounds monthly: **A = P(1 + r/n)^(nt).**

$10,000 * (1 + 0.04 percent / 12 times a year)^(12 times a year * 10 years) = $14908.32

- A = Final amount
- P = Initial principal balance
- r = Interest rate
- n = Number of times interest applied per time period
- t = Number of time periods elapsed

## How To Get Your Money to Compound?

**Savings accounts, certificates of deposit (CDs), and money market accounts.** The interest offered on these accounts will compound, although the interest rates are typically low. These types of investments are considered low-risk and offer lower returns.

**Investment accounts.** Many financial instruments like stocks, bonds, and REITs, regardless if they are held in regular brokerage accounts, retirement accounts, or education accounts, will compound over time. These types of investments are considered high-risk high-return investments.

Compounding returns is one of the most important investing concepts. Time is the crucial ingredient that makes compound interest work. With enough time, compounding can turn a small sum of money into a fortune.