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## What is compound interest?

The concept of compound interest, or 'interest on interest', is that accumulated interest is added back onto your principal sum, with future interest being calculated on both the original principal and the already-accrued interest. This compounding effect causes investments to grow faster over time, much like a snowball gaining size as it rolls downhill.

When you combine the power of interest compounding with regular, consistent investing over a sustained period of time, you end up
with a **highly effective growth strategy** for accelerating the long-term value of your savings or investments.

To demonstrate the effect of compounding, let's take a look at an example chart of an initial $1,000 investment. We'll use a 20 year investment term at a 10% annual interest rate, to keep things simple. As you compare the compound interest line to those for standard interest and no interest at all, you can see how compounding boosts the investment value.

So, how important is compound interest? Just ask Warren Buffett, one of the world's most successful investors:

Warren Buffett, 2010 5

## How is compound interest calculated?

Compound interest is a method that boosts your investment by adding earned interest back to the principal. This generates additional interest in the periods that follow, which accelerates your investment growth. So, when you earn interest on an investment, it isn’t just earned on the original amount; it’s calculated on the growing balance, including previously earned interest.

We'll explore an example later, to illustrate how it works. But before we do that, let's take a look at the formula.

### Understanding the formula

Compound interest is calculated using the **compound interest formula: A = P(1+r/n)^nt**.
For annual compounding, multiply the initial balance by one plus your annual interest rate raised to the power of
the number of time periods (years). This gives a combined figure for principal and compound interest.

Let's break the compound interest formula down into its individual parts:

Where:

- A = the future value of the investment
- P = the principal balance
- r = the annual interest rate (decimal)
- n = number of times interest is compounded per year
- t = the time in years
- ^ = ... to the power of ...

### How to calculate monthly compound interest

Here's how to calculate monthly compound interest using our compound interest formula. Monthly compound interest means that our interest is compounded 12 times per year:

- Divide your annual interest rate (decimal) by 12 and then add one to it.
- Raise the resulting figure to the power of the number of years multiplied by 12.
- Multiply your step 2 result by your principal balance (P).
- Deduct the principal balance from your step 3 result if you want just the interest.

As a formula, it looks like this:

A = P(1 + r/12)^12t

In our article about the compound interest formula, we go through the process of how to use the formula step-by-step, and give some real-world examples of how to use it.

## Using our interest calculator

You can use our compound interest calculator to do all the formula work for you. It'll tell you how much you might earn on your savings, investment or 401k over a period of years and months based upon a chosen number of compounds per year.

Simply enter your initial investment (principal amount), interest rate, compound frequency and the amount of time you're aiming to save or invest for. You can include regular deposits or withdrawals within your calculation to see how they impact the future value.

**See also:** Simple Interest Calculator | Loan Calculator With Extra Payments

## What will $10,000 be worth in 20 years?

We've discussed what compound interest is and how it is calculated. So, let's now break down interest compounding by year, using a more realistic example scenario. We'll say you have $10,000 in a savings account earning 5% interest per year, with annual compounding. We'll assume you intend to leave the investment untouched for 20 years. Your investment projection looks like this...

Year | Interest Calculation | Interest Earned | End Balance |
---|---|---|---|

Year 1 | $10,000 x 5% | $500 | $10,500 |

Year 2 | $10,500 x 5% | $525 | $11,025 |

Year 3 | $11,025 x 5% | $551.25 | $11,576.25 |

Year 4 | $11,576.25 x 5% | $578.81 | $12,155.06 |

Year 5 | $12,155.06 x 5% | $607.75 | $12,762.82 |

Year 6 | $12,762.82 x 5% | $638.14 | $13,400.96 |

Year 7 | $13,400.96 x 5% | $670.05 | $14,071 |

Year 8 | $14,071 x 5% | $703.55 | $14,774.55 |

Year 9 | $14,774.55 x 5% | $738.73 | $15,513.28 |

Year 10 | $15,513.28 x 5% | $775.66 | $16,288.95 |

Year 11 | $16,288.95 x 5% | $814.45 | $17,103.39 |

Year 12 | $17,103.39 x 5% | $855.17 | $17,958.56 |

Year 13 | $17,958.56 x 5% | $897.93 | $18,856.49 |

Year 14 | $18,856.49 x 5% | $942.82 | $19,799.32 |

Year 15 | $19,799.32 x 5% | $989.97 | $20,789.28 |

Year 16 | $20,789.28 x 5% | $1,039.46 | $21,828.75 |

Year 17 | $21,828.75 x 5% | $1,091.44 | $22,920.18 |

Year 18 | $22,920.18 x 5% | $1,146.01 | $24,066.19 |

Year 19 | $24,066.19 x 5% | $1,203.31 | $25,269.50 |

Year 20 | $25,269.50 x 5% | $1,263.48 | $26,532.98 |

**
$10,000 invested at a fixed 5% yearly interest rate, compounded yearly, will grow to $26,532.98 after 20 years. This means total interest of $16,532.98 and
a return on investment of 165%.
**

These example calculations assume a fixed percentage yearly interest rate. If you are investing your money, rather than saving it in fixed rate accounts, the reality is that returns on investments will vary year on year due to fluctuations caused by economic factors.

It is for this reason that the risk management strategy of diversification is widely recommended by industry experts.

## Compounding with additional deposits

Combining interest compounding with regular deposits into your savings account, SIP, Roth IRA or 401(k) is a highly efficient saving strategy that can really boost the growth of your money in the longer term. 4

Looking back at our example from above, if we were to contribute an additional $100 per month into our investment, our balance after 20 years would hit the heights of $67,121, with interest of $33,121 on total deposits of $34,000.

As financial institutions point out, if people begin making regular investment contributions early on in their lives, they can see significant growth in their savings further down the road as their interest snowball gets larger and they gain benefit from Dollar-cost or Pound-cost averaging. 5

## Where to invest for compound interest

The question about where to invest to earn the most compound interest has become a feature of our email inbox, with people thinking about mutual funds, ETFs, MMRs and high-yield savings accounts and wanting to know what's best.

We at The Calculator Site work to develop quality tools to assist you with your financial calculations. We can't, however, advise you about where to invest your money to achieve the best returns for you. Instead, we advise you to speak to a qualified financial advisor for advice based upon your own circumstances.

There are also some excellent articles from renowned financial websites that list ways to invest for compound interest. Here are two of the best articles, to help with your research:

- 13 Best Compound Interest Investments. WealthUp (author: Riley Adams).
- Accounts That Earn Compounding Interest. Motley Fool (author: Adam Levy).

## FAQ

Let's cover some frequently asked questions about our compound interest calculator.

### When is my interest compounded?

With savings and investments, interest can be compounded at either the start or the end of the compounding period. If additional deposits or withdrawals are included in your calculation, our calculator gives you the option to include them at either the start or end of each period.

### Can I include regular withdrawals?

You can include **regular withdrawals** within your compound interest calculation as either a monetary withdrawal or as a percentage of interest/earnings. This can be used in combination with
regular deposits.

You may, for example, want to include regular deposits whilst also withdrawing a percentage for taxation reporting purposes. Or,
you may be considering retirement and wondering **how long your money might last** with regular withdrawals.

### What is the effective annual interest rate?

The effective annual rate (also known as the annual percentage yield) is the rate of interest that you actually receive on your savings or investment after compounding has been factored in.

When interest compounding takes place, the effective annual rate becomes higher than the nominal annual interest rate. The more times the interest is compounded within the year, the higher the effective annual interest rate will be.

### What is RoR/TWR?

Within our compound interest calculator results section, you will see either a **RoR or TWR** figure appear for your calculation. You may be
wondering what these are, so let's take a look.

The **Rate of Return (RoR)** is the percentage return on your investment over the entire investment term. We calculate it by taking the Initial investment figure away from the Final value,
dividing the resulting figure by the Initial investment and then multiplying it by 100. The formula looks like this: 6

If you include regular deposits or withdrawals in your calculation, we switch to provide you with a **Time-Weighted Return (TWR) figure**.

The TWR figure represents the cumulative growth rate of your investment. It is calculated by breaking out each period's growth individually to remove the effects of any additional deposits and withdrawals. The TWR gives you a clearer picture of how your investment might have performed if you hadn't made extra deposits or withdrawn funds, allowing you to better assess its overall performance. You can learn more about TWR in this article by The Balance.

If you want to head back up to the calculator results area, you can click the link here. If you have any feedback or questions about the RoR or TWR, please contact us.

## Before you go...

**Here's a final thought**. If you want to roughly calculate compound interest on a savings figure, without using a calculator, you can use a formula called
the **rule of 72**. The rule of 72 helps you estimate the number of years it will take to double your money. The method is
simple - just divide the number 72 by your annual interest rate.

For example, let's say you're earning 3% per annum. Divide 72 by 3, which will give you 24. So, in about 24 years, your initial investment will have doubled. If you're receiving 6% then your money will double in about 12 years. All using the power of compound interest.

I hope you found this calculator and article useful. Many of the features in my compound interest calculator have come as a result of user feedback, so if you have any comments or suggestions, I would love to hear from you.

By Alastair Hazell Updated: June 26, 2024### References

- Edward Hubbard, Percival Matthews & Anya Samek (2016). Using online compound interest tools to improve financial literacy, The Journal of Economic Education.
- Lusardi and Tufano (2015); Lusardi and de Bassa Scheresberg (2013); Stango and Zinman (2009); Behrman et al., (2012); Lusardi and Mitchell (2014). Financial Literacy Around the World.
- The emergence of compound interest, British Actuarial Journal, 2019.
- How a small savings account can get big over time. Federal Deposit Insurance Corporation.
- How to take advantage of compound growth. Canada Life.
- Rate of return. CFI Education Inc.