# Compound Interest Calculator

Use our compound interest calculator to see how the power of compound interest can grow your savings or investments over time.

**Disclaimer:** Whilst every effort has been made in building this tool, we are not to be held
liable for any damages or monetary losses arising out of or in connection with the use of it. Full disclaimer.
This tool is here purely as a service to you, please use it at your own risk.

**On this page:**

## How to calculate compound interest

Compound interest is calculated using the compound interest formula. To calculate your future value, multiply your initial balance by one plus the annual interest rate raised to the power of the number of compound periods. Subtract the initial balance if you want just the compounded interest figure.

^{(nt)}

Where:

- A = the future value of the investment or loan
- P = the principal investment or loan amount
- r = the interest rate (decimal)
- n = the number of times that interest is compounded per period
- t = the number of periods the money is invested for

You can use a **compound interest calculator** to create a projection of how much your savings or investments might grow over a period of time using the
power of compound interest. We have a separate article discussing variations of the compound interest formula, should you be interested.

## Using our interest calculator

Our interest calculator gives you a future balance and a projected monthly and yearly breakdown for the time period. Here's how to use it:

- Enter an initial balance figure
- Enter a percentage interest rate - either yearly, monthly, weekly or daily
- Enter a number of years or months, or a combination of both, for the calculation
- Select your compounding interval (daily, monthly, quarterly or yearly compounding)
- Include any regular monthly, quarterly or yearly deposits or withdrawals

You can use the results as a guide to create a saving strategy to maximise your future wealth. Should you wish to make a calculation without compounding, give our simple interest calculator a try.

## 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 calculations being carried out on the total of both the original principal and already-accrued
interest. According to an article published in the Journal of Economic Education in 2016, less than one-third of the U.S. population comprehends how compound
interest fundamentally works ^{1}.

The idea of compound interest has been around a long time, with limited evidence suggesting ancient civilizations may even have known about it. At the Louvre in Paris, there exists a clay tablet from Babylon, possibly
dating from between 2000 to 1700 B.C., which appears to show a compound interest problem. However, it seems likely that it wasn't until medieval times that
mathematicians began to analyse compound interest fully ^{2}.

## Compound interest example

Let's look at a simple example and say you have $10,000 in your savings account, earning 5% interest per year. Your first 10 years might look 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 |

Let's look at how we can calculate the year 10 figure using our formula. Remember that our initial savings balance is $10,000, earning 5% interest per year. Our compounding in this case is yearly (interest compounded once per year).

Our formula: **A = P(1+r/n) ^{(nt)}**

- P = 10000.
- r = 5/100 = 0.05 (decimal).
- n = 1.
- t = 10.

If we plug those figures into the formula, we get the following:

^{ (1 × 10)}= 16288.95

So, the balance after 10 years is $16,288.95. Our total interest earned is therefore $6,288.95.

## Compounding with additional deposits

If you get into a pattern of making regular deposits into your savings, the power of compound interest can help you achieve even higher interest rewards. Looking back at the example above, if we were to contribute an additional $100 per month into our investment, our balance after 10 years would hit the heights of $31,725, with interest of $9,725 on total deposits of $22,000.

## Compound interest chart

The power of compound interest really becomes apparent when you look at a chart of long-term growth. Here's an example chart. You invest your profit margin from a sale of an item ($1,000). We'll use a longer compounding investment period (20 years) at 10% per year, to keep the sum simple. As we compare the benefits of compound interest versus standard interest and no interest at all, it's clear to see how compound interest can really give a boost to your savings.

## FAQ

Some frequently asked questions about calculating interest and my savings calculators.

### When is interest compounded?

With savings accounts, 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, you have the option to include them either at the start or end of each period.

### Daily, monthly or yearly interest compounding

Our compound interest calculator includes options for:

- daily compounding
- monthly compounding
- quarterly compounding
- half yearly and yearly compounding
- monthly, quarterly and yearly deposits and withdrawals
- negative interest rates
- inflation increases

Your savings account may vary on this, so you may wish to check with your bank or financial institution to find out which frequency they compound your interest at. Our compound interest calculator allows you to enter a negative interest rate, should you wish. If you need to work out the interest due on a loan, you can use the loan calculator.

### What is the effective annual interest rate?

The effective annual rate is the rate of interest that you actually receive on your savings after inclusion of compounding. When compounding of interest 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 rate will be.

## Further reading

You can learn more about the power of interest compounding in our article, what is compound interest?. If you're currently studying at university, you may also find our uni grade calculator useful for calculating your module or degree grades.

Calculator created by Alastair Hazell and reviewed by James Whittington.Calculator references: