# Compound Interest Calculator

\$

This option lets you hide the advanced options if you don’t want them. We will remember your choice.
\$
\$
Deposits made at what point in period?
Increase deposits yearly with inflation?
Use our compound interest calculator to project the future value of your savings or investments over time.

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.

## 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.

### The compound interest formula

A = P(1+r/n)^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
• ^ = ... to the power of ...

Combining the power of interest compounding with regular, consistent investing over a sustained period of time can be a highly effective approach for increasing your wealth - a strategy of compound growth.

You can use a compound interest calculator to project how much your money might grow over time. It creates a projection for compound growth for your savings account or investment over a time period, based upon an anticipated rate of interest.

## 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

A 2015 study looking at insights from the S&P’s Global Financial Literacy Survey found that “consumers who fail to understand the concept of interest compounding spend more on transaction fees, run up bigger debts, and incur higher interest rates on loans.” They also end up borrowing more and saving less money. Meanwhile, it comes as little surprise that those who possess more financial knowledge and skills are better at planning and saving for future retirement. 2

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. 3

The power of compound interest really becomes apparent when you look at a chart of long-term growth. Below is an example chart of an initial \$1000 investment. 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 help boost your investment value.

The following are examples of investments where interest can be compounded for growth:

• Savings accounts
• Money market accounts
• Dividend stocks
• Roth IRA
• 401(k)
• ISA (UK)
• Cryptocurrency investing

## How to use our compound interest calculator

Our compound interest calculator shows you how much the money you invest or save could grow over time. It gives you a future balance and a projected monthly and yearly interest breakdown for the time period. Here's how to use it:

1. Enter an initial balance figure
2. Enter a percentage interest rate - either yearly, monthly, weekly or daily
3. Enter a number of years or months, or a combination of both, for the calculation
4. Select your compounding interval (daily, monthly, quarterly or yearly compounding)
5. 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.

## Example of compound growth

Let's look at a simple example and say you have \$10,000 in your savings or investment 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:

A = 10000 (1 + 0.05 / 1) ^ (1 × 10) = 16288.95

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

## Consistent, regular saving

Combining interest compounding with a pattern of making regular deposits into your savings account, Roth IRA or 401(k) is something that can really pay off for you in the longer term. Looking back at the example we've given 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.

As financial institutions point out, if someone begins making regular investment contributions early on in their lives they can see significant growth in their savings value further down the road as their interest snowball gets larger and they gain benefit from Dollar-cost or Pound-cost averaging. 4

## FAQ

### When is interest compounded?

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

### Can I include 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, wish to be contributing regular deposits whilst also withdrawing an amount for taxation reporting purposes. Or, you may be considering retirement and wondering how long your money might last with regular percentage-of-balance withdrawals.

### Daily, monthly or yearly interest compounding

Our compound interest calculator includes options for:

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

Your investment 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.

Our interest calculator is multi-currency, allowing you to create projections using the following currencies:

• \$ - Dollar (US, Australia, etc)
• £ - Pound (UK)
• € - Euro (Europe)
• ₹ - Rupee (India)
• ¥ - Yen (Japan)

Should you wish to use a currency that isn't included in these options, please use the blank currency box.

### What is the effective annual interest rate?

The effective annual rate is the rate of interest that you actually receive on your savings or investment 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 interest rate will be.

Calculator by Alastair Hazell. Reviewed by James Whittington.

### Calculator 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. Saving earlier can help give you the power of compound interest on your savings. Canada Life.