Compound interest

Introduction

Compound interest is one of the most important concepts to understand when investing for the long term. It describes a simple but powerful process: your money generates returns, those returns remain invested, and future returns can then be earned on a larger amount.

At first, the difference may seem small. Over longer periods, however, compounding can have a significant impact on how an investment grows.

Time plays an especially important role. The longer money has the opportunity to compound, the greater the potential effect can become. This is one reason why starting early can be so valuable, even when the initial amount invested is relatively small.

In this article, we will look at how compound interest works, how it is calculated, and why time, returns, and regular contributions can make such a difference for long-term investors.

This is the basic idea behind compounding.

In investing, the concept is slightly different because investments generally do not provide a fixed rate of interest. However, a similar compounding effect can occur when investment returns remain invested and have the opportunity to generate additional returns in the future.

What is compound interest?

Compound interest means that interest is earned not only on your original amount of money, but also on the interest that has already accumulated.

Suppose you deposit $10,000 into an account that earns 5% interest per year. After the first year, you earn $500, bringing your total balance to $10,500.

If the interest remains in the account, the calculation changes in the second year. Instead of earning 5% on the original $10,000, you now earn 5% on $10,500. This results in $525 of interest and increases your balance to $11,025.

The additional $25 may not seem particularly important. But the same process can continue year after year, with interest being calculated on an increasingly larger balance.

How compound interest works

A simple example can make compounding easier to understand.

Imagine that you invest $10,000 and earn a hypothetical return of 8% each year. You do not withdraw any of the returns.

After the first year, your investment would have grown by $800 to $10,800.

During the second year, the 8% return would be calculated on $10,800 instead of $10,000. This would produce $864 in returns and increase the investment to $11,664.

The process continues as follows:

Notice that the assumed return remains 8% throughout the example, but the amount earned each year becomes larger.

In the first year, the investment earns $800. By the fifth year, the same 8% return produces approximately $1,088.

This happens because the returns from previous years have remained invested. As the investment becomes larger, the same percentage return represents a larger dollar amount.

The compound interest formula

Compound interest can be calculated using a relatively simple formula:

FV = PV × (1 + r)ⁿ

The different parts of the formula represent:

• FV (Future Value): the value of the investment at the end of the period
• PV (Present Value): the amount you start with
• r: the rate of return or interest rate per period
• n: the number of periods

For example, suppose you invest $10,000 at an annual rate of 8% for 20 years.

The calculation would be:

$10,000 × (1.08)²⁰ = $46,610

Assuming the 8% rate remained constant and all returns were reinvested, the original $10,000 would grow to approximately $46,610 after 20 years.

The most important part of this formula for long-term investors is the exponent. Each additional period gives previous returns another opportunity to generate returns of their own.

The compound interest formula

Simple interest and compound interest both allow money to grow, but they calculate that growth differently.

With simple interest, interest is calculated only on the original amount. Previously earned interest does not increase the amount on which future interest is calculated.

With compound interest, previously earned interest is added to the balance. Future interest can therefore be earned on both the original amount and accumulated interest.

Consider an initial amount of $10,000 earning 8% annually for 20 years.

With simple interest, you would earn $800 every year. After 20 years, you would have earned $16,000 in interest, resulting in a total of $26,000.

With annual compound interest, the same $10,000 would grow to approximately $46,610.

The difference becomes increasingly significant as more time passes because compound growth builds on itself.

Why Time Matters So Much

Time is one of the most important ingredients in compounding.

The effect is not simply that an investment has more years to earn returns. Each additional year also allows previous returns to potentially generate new returns.

Consider what happens to a $10,000 investment earning a hypothetical 8% annual return:

After the first 10 years, the investment has grown by approximately $11,589.

Between years 30 and 40, however, the investment grows by more than $116,000. No additional money has been invested in this example. The difference comes entirely from allowing an increasingly larger amount to continue compounding.

This demonstrates an important characteristic of compound growth: it is exponential rather than linear.

The early years can sometimes appear relatively slow. As more returns accumulate, however, the amount available to generate future returns becomes increasingly larger.

This is why starting earlier can provide a major advantage. An investor who starts with a smaller amount but has several additional decades available may benefit significantly from the extra compounding time.

The impact of your rate of return

Time is not the only factor that determines how quickly an investment can grow. The rate of return also has a significant impact.

Small differences in annual returns may not appear particularly important over a single year. Over several decades, those differences can become substantial.

Consider an initial investment of $10,000 held for 30 years:

The difference between a 6% and an 8% annual return is only two percentage points. Yet after 30 years, the difference in the ending value is more than $43,000.

At 10%, the hypothetical ending value is more than three times the value produced by a 6% return.

However, higher expected returns generally come with higher investment risk. Investors should not simply pursue the highest possible return in an attempt to maximize compounding.

It is also important to remember that these examples assume a constant annual return. Real investment returns fluctuate. Some years may produce gains, while others may result in losses. These examples are intended to demonstrate how compounding works rather than predict actual investment performance.

The power of regular contributions

Compounding can become even more powerful when new money is regularly added to an investment.

Many investors do not invest one large amount and then leave it untouched for several decades. Instead, they contribute money regularly, often every month.

Suppose you begin with $10,000 and earn a hypothetical average return of 8% annually for 30 years.

Without making any additional contributions, the initial $10,000 would grow to approximately $100,627.

Now imagine that you also contribute $200 each month.

Over 30 years, you would personally contribute $82,000 in total, consisting of the initial $10,000 plus $72,000 in monthly contributions. With an assumed 8% annual return compounded monthly, the investment could grow to approximately $399,000.

A substantial part of the final value would therefore come from investment growth rather than contributions alone.

Regular investing has two important effects. First, you continuously add new capital to your portfolio. Second, earlier contributions have more time to potentially generate returns of their own.

This combination of regular contributions and long-term compounding can have a significant impact on wealth accumulation.

How compounding frequency works

Interest does not always compound annually. Depending on the financial product, compounding can occur at different intervals.

Common compounding frequencies include:

• Annually
• Quarterly
• Monthly
• Daily

If all other factors are equal, more frequent compounding generally results in a slightly higher ending balance because accumulated interest begins earning additional interest sooner.

For example, an account paying 5% interest compounded monthly will produce slightly more than an account paying 5% once per year, assuming the quoted rates are otherwise comparable.

For long-term investors, however, the difference between monthly and annual compounding is usually less important than factors such as the amount invested, investment returns, fees, and the amount of time the money remains invested.

Compounding frequency is also more directly applicable to interest-bearing products. Stocks, ETFs, and other market investments do not normally generate a fixed rate of interest at predetermined intervals.

Compound interest and investing

The term compound interest is often associated with savings accounts, bonds, and other interest-bearing investments. When discussing stocks and other market investments, compound growth or compounding returns is often a more accurate description.

The underlying principle, however, is similar.

Stocks

Suppose a stock increases in value and you continue holding it. Any future percentage gain is now applied to the higher value of your investment.

If a $10,000 stock investment increases by 10%, it becomes worth $11,000. Another 10% increase would represent $1,100 rather than the original $1,000.

This creates a compounding effect as long as gains remain invested.

Of course, stock prices can also decline. Unlike a savings account with a fixed interest rate, investment returns are uncertain and can vary significantly from year to year.

Dividend Stocks

Compounding can also occur when dividends are reinvested.

Instead of taking dividend payments as cash, an investor may use them to purchase additional shares. Those additional shares can then potentially generate their own dividends in the future.

Repeated over many years, dividend reinvestment can increase both the number of shares owned and the amount of future dividend income generated by the investment.

ETFs

A similar principle applies to exchange-traded funds.

Returns that remain invested can continue participating in future market growth. Distributions can also be reinvested, either automatically or manually, depending on the ETF and brokerage account.

Savings and Bonds

With traditional interest-bearing products, compound interest works more directly.

Interest is added to the principal, increasing the balance on which future interest may be calculated. This is the classic form of compound interest and is generally easier to predict when the interest rate is fixed.

What can reduce the effect of compounding?

Compounding can be powerful, but several factors can reduce its long-term effect.

A compound growth example

Let’s look at a longer-term example.

Suppose an investor starts with no initial investment and contributes $250 at the end of every month for 30 years. For illustration, we will assume an average annual return of 8%, compounded monthly.

Over those 30 years, the investor would personally contribute:

$250 × 12 × 30 = $90,000

However, the final investment value would be approximately $373,000 under these assumptions.

This means that roughly $283,000 of the ending value would come from investment growth rather than the money contributed by the investor.

The example demonstrates why both consistency and time can be so important.

During the early years, most of the portfolio consists of the investor’s own contributions. As time passes, investment growth can represent an increasingly large part of the portfolio.

This is also why compounding is usually most noticeable over long periods. It takes time for accumulated returns to become large enough to generate substantial additional returns of their own.

Actual investment performance will not follow this smooth path. Returns fluctuate, and an 8% average annual return is not guaranteed.

How to take advantage of compounding?

You cannot control future market returns, but there are several ways investors can give compounding more opportunity to work.

Key Takeaways

Compound interest is a simple concept with potentially significant long-term effects.

Instead of earning interest only on the original amount, compound interest allows previously accumulated interest to generate additional interest. In investing, a similar effect can occur when returns remain invested and continue participating in future growth.

The most important things to remember are:

• Compounding builds on previous growth. Returns that remain invested can potentially generate additional returns.
• Time plays a major role. The longer money has to compound, the greater the potential effect can become.
• The rate of return matters. Small differences in annual returns can lead to large differences over several decades.
• Regular contributions can accelerate portfolio growth. Adding money consistently increases the amount available to generate future returns.
• Fees, taxes, withdrawals, inflation, and investment losses can reduce compound growth.
• Investment returns are not guaranteed. Real markets fluctuate, so actual investment growth will not follow the smooth examples used in compound interest calculations.

Compounding is rarely dramatic in the short term. Its real strength becomes visible when money is given enough time to grow. For long-term investors, understanding this principle can help explain why starting early, investing consistently, and allowing returns to remain invested can make such a meaningful difference over time.