# Compound Interest Calculator

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By Alastair Hazell. Reviewed by Chris Hindle.
Deposits made at what point in period?

Use our interest calculator to calculate the possible growth of your savings and investments over time. We discuss what compound interest is and how it can help you reach your financial goals in our article below.

Disclaimer: Whilst every effort has been made in building our calculator tools, we are not to be held liable for any damages or monetary losses arising out of or in connection with their use. Full disclaimer.

## Using our interest calculator

With our compound interest calculator you can calculate the interest 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.

### 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 made on both the original principal and the already-accrued interest.

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.

Here’s a short video explaining how compound interest works…

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

“My wealth has come from a combination of living in America, some lucky genes, and compound interest.”

Warren Buffett, 2010 5

## How is compound interest calculated?

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:

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

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:

1. Divide your annual interest rate (decimal) by 12 and then add one to it.
2. Raise the resulting figure to the power of the number of years multiplied by 12.
4. 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.

For the remainder of the article, we'll look at how compound interest provides positive benefits for savings and investments.

### The benefits of compound interest

I think pictures really help with understanding concepts, and this situation is no different. The power of compound interest becomes obvious when you look at a graph of long-term growth.

Below is an example graph of an initial \$1,000 investment. We'll use a longer investment compounding period (20 years) at 10% per year, to keep the sum simple.

As we compare the compound interest line in our graph to those for standard interest and no interest at all, it's clear to see how compound interest boosts the investment value over time.

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

Let's break down the interest compounding by year with 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.

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:

## FAQ

### 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.

## 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.

Updated: December 9, 2022

### References

1. Edward Hubbard, Percival Matthews & Anya Samek (2016). Using online compound interest tools to improve financial literacy, The Journal of Economic Education.
2. 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.
3. The emergence of compound interest, British Actuarial Journal, 2019.
4. How a small savings account can get big over time. Federal Deposit Insurance Corporation.
5. Saving earlier can help give you the power of compound interest on your savings. Canada Life.

From abacus to iPhones, learn how calculators developed over time.