• Smart Cash
• Performance
• Get Started

How does compound interest work?

Origin of compound interest

How to calculate compound interest

Simple vs. compound interest

How does compound interest work with stocks and mutual funds?

The bottom line

LearnRate of ReturnWhat Is Compound Interest?

# What Is Compound Interest?

Aug 31, 2022

·

Compound interest works by using the continual multiplication—or compounding—of an amount of money, over a set number of cycles, within a set period of time.

It’s believed that Albert Einstein once called compound interest the eighth wonder of the world: “He who understands it, earns it. He who doesn't, pays it.” This article will explain compound interest and teach you how to calculate it, as you look to grow your wealth.

To understand compound interest, let’s take a step back. Interest is, in the plainest terms, the cost of borrowing money. When you borrow money, you pay interest: a set percentage owed on top of the principal you borrowed. When you lend money, you receive interest: a set percentage received on top of your principal. Compound interest occurs when that initial interest compounds along with your principal.

By way of example: If your principal investment of \$100 receives 10% interest per annum, you have \$110 at the end of the year. That \$110 then receives 10% interest per annum, leaving you with \$121 at the end of the second year. That \$121 then receives 10% interest per annum, so you’ll have \$133.10 at the end of the third year. In other words, the amount of interest you receive is growing each year, compounding along with your principal and exponentially growing your wealth.

## How does compound interest work?

Compound interest works by using the continual multiplication—or compounding—of an amount of money, over a set number of cycles, within a set period of time. The interest paid is added to your original pile of money, on which the next interest payment is calculated. You are earning interest on interest, and your initial wealth begets more and more wealth as a result.

Each time interest is paid, it’s added to your principal—the money you started with—helping that pile of money grow. Interest for the next compounding period is then calculated on this larger principal. This compounding continues for the duration of the agreement, or can continue with no end date.

## Origin of compound interest

As early as the 13th century, European mathematicians created massive tables and grids of numbers designed to solve questions such as: How much should a person be charged in exchange for a contract directing payment of an annual sum for each year of the person’s life? These tables were also used to calculate annuities, loan rates, and many types of contracts.

In certain contracts, interest due on a loan may automatically be added to the loan balance. So just as compounding can work in favor of an investor who is able to save, the opposite can be true for those who borrow. For example, a credit card balance can swiftly grow almost out of control because interest charges can pile up at an accelerating rate.

## How to calculate compound interest

The central mathematical concept of compounding hinges on the idea of future value. What is something going to be worth in the future, and, conversely, what should something be worth today, to pay out, or receive, a certain sum, sometime in the future?

Here’s a basic compound interest calculator that shows examples of how compound interest works.

Consider a customer who deposits \$1,000 into a savings account that earns 2% per year. We’ll calculate the compound interest for a variety of time periods.

Similarly, using the example above, consider that your \$1,000 was used to purchase a stock that paid a 2% annual dividend, which is paid quarterly. If the value of the stock stayed constant at \$1,000, your investment value would be the same.

## Compound interest formula

Investments that generate compound interest rely on calculations involving four components:

1. The initial principal (for example, that pile of money you invested at the start).
2. The interest rate (the cost of the money or the dividend yield).
3. The number of times interest or dividends are paid during the life of the investment. If the annual interest rate is 2% per year, and payments are made quarterly (every three months), you’re already earning compound interest on your principal after the very first payment or dividend.
4. And finally, the time periods covered by the investment or agreement.

Here’s a breakdown of the formula where P is the principal, or present value of \$1,000, earning an interest rate of 2% (r for rate) per year, with payments made every three months—or four times a year—(n is the number of times per period interest is paid), for 10 years (t for the time period).

This is expressed as the formula:

A = P(1 + r/n)nt

Where A is the total amount of principal and accrued interest.

## Calculating compound interest in Excel

Let’s use a spreadsheet to automate and simplify our calculations:

First, in our example, there are 40 payment periods, four per year for 10 years. We put that number in cell B2. We know the annual interest rate is 2%, so we enter that in cell B3. There are no payments being made other than the initial principal invested of \$1,000, so we enter 0 for payments. Now we consider that the investor puts \$1,000 into the account, and therefore the present value is entered as a negative number of -1,000.

We don’t know what the future value is, so we leave that blank. Finally, we enter 4 for the number of periods payments will be made each year.

Now we can use the spreadsheet formula FV for future value. Click in cell C6 and type the formula =FV(B3/B7, B2, B4, B5) and hit return.

You will see that the FV function has done the calculation for you. You can also adjust all of the inputs to apply different time periods, principal amounts, or rates of interest. It’s a tool to compute compound interest in a variety of scenarios.

Now, let’s plug our numbers into the compound interest formula and check the accuracy of our Excel function

First, convert r, or rate, from a percent to a decimal.

r = r/100

r = 2/100

r = 0.02 rate per year

Then solve the equation for A, based on the formula cited above:

A = 1,000.00(1 + 0.02/4)(4)(10)

A = 1,000.00(1 + 0.005)(40)

A = \$1,220.79

A = P + I where

P (principal) = \$1,000.00

I (interest) = \$220.79

A, the total amount accrued, principal plus interest, with compound interest on a principal of \$1,000.00 at a rate of 2% per year, compounded four times per year over 10 years is \$1,220.79.

You can see that compounding makes your money grow faster because the interest is calculated on the accumulated interest as well as your original principal. Compound interest creates a snowball effect, as your original investment, plus the interest earned from those investments, grow hand-in-hand.

## Simple vs. compound interest

Now let’s compare what our investment value would be using the simple interest formula versus the compound interest formula.

Simple interest is only calculated on the principal amount—it doesn’t include interest accrued over time.

We’ll use the same example of \$1,000 invested at 2% a year, with four payments per year for 10 years. Here’s the simple interest formula:

A = P (1+rt)

A = the total accrued amount (the principal + the interest)
P = the principal of \$1,000
I = the interest rate of 2% which is \$20, or \$5 every quarter
r = rate of interest per year expressed in decimal form
t = the time period involved in months or years

A = \$1,000(1 + 0.02*10)
A = \$1,200 after 10 years

You would earn just \$1,200 with simple interest over the same period of time, while with compound interest you accumulate 10% more, or \$1,220.79.

Compound interest is traditionally associated with money held in savings and checking accounts at banks, but because we’re in a period of extended low-interest rates, the benefits of compounding at a bank are pretty negligible. But dividend-paying stocks can provide similar advantages.

Try Titan’s free Compound Interest Calculator to see how compounding could affect your investment returns.

## How does compound interest work with stocks and mutual funds?

Dividend-paying stocks and mutual funds can enable you to earn compound interest on your investments, as long as a dividend reinvestment plan is available and selected.

Dividend reinvestment plans work by using the dividends you receive from your investment to purchase additional shares. In other words, when your investment in Company X pays out dividends, the dividend reinvestment plan takes that capital to purchase more Company X shares. As long as Company X’s stock continues to pay dividends, you end up with more shares—and more dividends paid —each cycle.

The advantages of compounding are even greater when the stocks, or other interest-bearing assets, are held in a tax-advantaged account, such as an IRA (Individual Retirement Account).

Tax-advantaged accounts allow investors to shield the compounding value of your investments from tax liabilities, until funds are withdrawn.

By deferring your tax liability, your principal may be able to grow larger and faster. The dividends paid on the accumulated investment in a pretax account will be greater than if they were paid on aftertax holdings. This, in turn, leads to a faster accumulation of wealth.

## The bottom line

Now that you understand more about compound interest and how to calculate it, it should be clear how a consistent savings plan, leaving income in an account where it is compounded, is a fundamental tenet to growing your wealth. And the more time compounding has to work its magic, the more money you’ll have.

At Titan, we are value investors: we aim to manage our portfolios with a steady focus on fundamentals and an eye on massive long-term growth potential. Investing with Titan is easy, transparent, and effective.

Get started today.

Disclosures

Certain information contained in here has been obtained from third-party sources. While taken from sources believed to be reliable, Titan has not independently verified such information and makes no representations about the accuracy of the information or its appropriateness for a given situation. In addition, this content may include third-party advertisements; Titan has not reviewed such advertisements and does not endorse any advertising content contained therein.

This content is provided for informational purposes only, and should not be relied upon as legal, business, investment, or tax advice. You should consult your own advisers as to those matters. References to any securities or digital assets are for illustrative purposes only and do not constitute an investment recommendation or offer to provide investment advisory services. Furthermore, this content is not directed at nor intended for use by any investors or prospective investors, and may not under any circumstances be relied upon when making a decision to invest in any strategy managed by Titan. Any investments referred to, or described are not representative of all investments in strategies managed by Titan, and there can be no assurance that the investments will be profitable or that other investments made in the future will have similar characteristics or results.

Charts and graphs provided within are for informational purposes solely and should not be relied upon when making any investment decision. Past performance is not indicative of future results. The content speaks only as of the date indicated. Any projections, estimates, forecasts, targets, prospects, and/or opinions expressed in these materials are subject to change without notice and may differ or be contrary to opinions expressed by others. Please see Titan’s Legal Page for additional important information.

Three Things, a newsletter from Titan

Stay informed on the most impactful business and financial news with analysis from our team.

You might also like

How to Calculate Rate of Return on Investments

Rate of return allows us to make clear comparisons among investments, which is essential. It puts them on a common scale.

What Is a Rate of Return?

Simply put, the rate of return (ROR) is the gain or loss for any investment, in percentage terms, for a given period of time.

What Is Annual Percentage Rate (APR)?

The APR takes into account interest rate and any fees a lender may charge for issuing a personal loan or mortgage, or for credit cards, any unpaid balance.

What Is the Rule of 72?

The Rule of 72 is an easy, concise equation that calculates the amount of time your investment will need to increase its value twofold.

Cash Management

Smart Cash

Smart Cash FAQs

Cash Options

Get Smart Cash

Titan Global Capital Management USA LLC ("Titan") is an investment adviser registered with the Securities and Exchange Commission (“SEC”). By using this website, you accept and agree to Titan’s Terms of Use and Privacy Policy. Titan’s investment advisory services are available only to residents of the United States in jurisdictions where Titan is registered. Nothing on this website should be considered an offer, solicitation of an offer, or advice to buy or sell securities or investment products. Past performance is no guarantee of future results. Any historical returns, expected returns, or probability projections are hypothetical in nature and may not reflect actual future performance. Account holdings and other information provided are for illustrative purposes only and are not to be considered investment recommendations. The content on this website is for informational purposes only and does not constitute a comprehensive description of Titan’s investment advisory services.

Please refer to Titan's Program Brochure for important additional information. Certain investments are not suitable for all investors. Before investing, you should consider your investment objectives and any fees charged by Titan. The rate of return on investments can vary widely over time, especially for long term investments. Investment losses are possible, including the potential loss of all amounts invested, including principal. Brokerage services are provided to Titan Clients by Titan Global Technologies LLC and Apex Clearing Corporation, both registered broker-dealers and members of FINRA/SIPC. For more information, visit our disclosures page. You may check the background of these firms by visiting FINRA's BrokerCheck.

Various Registered Investment Company products (“Third Party Funds”) offered by third party fund families and investment companies are made available on the platform. Some of these Third Party Funds are offered through Titan Global Technologies LLC. Other Third Party Funds are offered to advisory clients by Titan. Before investing in such Third Party Funds you should consult the specific supplemental information available for each product. Please refer to Titan's Program Brochure for important additional information. Certain Third Party Funds that are available on Titan’s platform are interval funds. Investments in interval funds are highly speculative and subject to a lack of liquidity that is generally available in other types of investments. Actual investment return and principal value is likely to fluctuate and may depreciate in value when redeemed. Liquidity and distributions are not guaranteed, and are subject to availability at the discretion of the Third Party Fund.

The cash sweep program is made available in coordination with Apex Clearing Corporation through Titan Global Technologies LLC. Please visit www.titan.com/legal for applicable terms and conditions and important disclosures.

Cryptocurrency advisory services are provided by Titan.

Information provided by Titan Support is for informational and general educational purposes only and is not investment or financial advice.

Contact Titan at support@titan.com. 508 LaGuardia Place NY, NY 10012.