# What is Compound Interest?

##### By: Mark Gregorski
Aug 22, 2024 5 min read

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Compound interest is the combined interest earned on the original principal amount and on the accumulated interest from prior periods.

It’s one of the most fundamental concepts in personal finance.

Compound interest can have a massive impact on both your ability to build wealth and the amount you pay on borrowed money.

## Compound Interest Definition

Compound interest refers to the interest on the initial principal plus the interest accumulated from past periods.

Before the next interest amount is calculated, the interest previously earned is added to the principal.

This cycle of adding the accrued interest to the principal continues for each period.

For this reason, it’s suitable to conceptualize compound interest as the “interest earned on interest.”

Compound interest applies to both investment and loan products.

Did You Know?

The Rule of 72 (72 ÷ assumed rate of return) is a quick and easy way to estimate how long it will take for your money to double in value.

## Compound Interest Formula

The formula for calculating compound interest is relatively straightforward.

You multiply the original principal by one, plus the annual interest rate raised to the number of periods, minus one.

Here’s the breakdown of the formula:

Compound Interest = P [(1 + i)n – 1]

Where:

P = Principal

i = annual interest rate expressed as a decimal

n = number of compounding periods

An example will help to illustrate how the formula works.

Suppose that you deposit \$5,000 into an investment account that yields a return of 4%, compounded annually.

What would be the total interest you earn after three years?

Using the above formula, we can determine that you’d earn \$624.32 in interest:

\$5,000 [(1 + 0.04)3 – 1] =

\$5,000 [1.124864 – 1] =

\$5,000 [0.124864] =

\$624.32

An important aspect to understand regarding compound interest is compounding frequency.

This factor measures how quickly accumulated interest is added to the principal before the new interest calculation occurs.

There are many different rates at which interest can compound: annually, quarterly, monthly, daily, etc.

The frequency used depends mainly on the type of investment product.

The concept applies equally to various loans, such as mortgages, auto loans, and credit cards.

The interest you earn is added to the principal once per year in the example above.

Let’s assume, instead, that the interest compounds monthly.

In that case, we would modify the formula slightly by dividing the annual interest rate by the number of times it compounds per year.

Also, we would need to multiply the number of compounding periods per year by the number of years we plan to hold the investment.

Thus, the amount of interest you’d earn after three years would be \$636.36, which is only slightly higher, but can make a large difference over a longer period of time.

\$5,000 [(1 + 0.04 / 12)(3)(12) – 1] =

\$5,000 [(1 + 0.003333333)36 – 1] =

\$5,000 [1.127272 – 1] =

\$5,000 [0.127272] =

\$636.36

## How Does Compound Interest Work?

Below is an example that showcases the “magic” of compound interest based on an initial investment of \$100,000 that earns various rates of return, compounded annually:

5% 10% 15%
Year 1 \$105,000.00 \$110,000.00 \$115,00.00
Year 2 \$110,250.00 \$121,000.00 \$132,250.00
Year 3 \$115,762.50 \$133,100.00 \$152,087.50
Year 4 \$121,550.63 \$146,410.00 \$174,900.63
Year 5 \$127,628.16 \$161,051.00 \$201,135.72
Year 10 \$162,889.46 \$259,374.25 \$404,555.77
Year 20 \$265,329.77 \$672,749.99 \$1,636.653.74

## Why is Compound Interest Important?

Here are some reasons why it pays to get acquainted with compound interest.

Saving for the long term can be an arduous and sluggish process.

It can take many years, often decades, until you hit your savings target.

Simply squirrelling away money in a zero-interest chequing account won’t suffice, especially if you don’t have the luxury of time on your side.

When coupled with wise investment selection and consistent deposits, compound interest can accelerate your investment growth, enabling you to reach your savings goals sooner.

### 2. Its benefits only become apparent with time

You won’t reap the rewards of compound interest until after many years, which is why it’s wise to kickstart your savings and investment plan as soon as possible.

The earlier you begin to amass your wealth, the better.

### 3. It helps you maintain your quality of life

Compound interest can be a valuable tool to help you stave off inflation’s pernicious effects by steadily growing your wealth to keep pace with it.

Without it, your money will continue to lose value, year after year.

### 4. It can increase your debt burden

The interest on various loan products is subject to compounding.

As a result, it can substantially increase your total debt over time, especially if you fall behind on payments.

The prospect of burdensome debt should incentivize you to increase the pace you pay it down.

Fact

The interest charged by the Canada Revenue Agency (CRA) on past due balances owing compounds daily!

## What’s the Difference Between Simple Interest and Compound Interest?

The difference between simple interest and compound interest is that the rate of return on the former is calculated only on the principal.

In contrast, the rate of return on the latter is calculated on the principal plus accumulated interest from previous periods.

For example, suppose you decide to invest \$1,000 for five years into an account that pays an annual interest rate of 5%.

If the deposit earns investment income according to simple interest, you’d realize interest income of \$250 at the end of five years.

In other words, the account would earn \$50 each year (\$1,000 x 0.05) since the rate of return is based only on the original principal.

Let’s assume the same investment compounds yearly.

In that case, you’d earn \$276.28 in interest over the five years.

The interest you earn is added to your initial principal at the end of each year.

As a result, the interest calculation in each subsequent year is based on increasingly larger sums.

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## How do you calculate compound interest?

The formula to calculate compound interest is as follows: P [(1 + i/n)nt – 1] Step 1: Divide the annual interest rate (i) by the number of compounding periods per year (n) and add one Step 2: Raise the resulting figure to the number of compounding periods in your time frame (t) and deduct one Step 3: Multiply the resulting figure by the original principal (p)

## When is compound interest used?

Compound interest is applied widely to many investment and loan products. It's a core component of many long-term investment strategies, especially those that utilize a tax-advantaged account, like an RRSP, where income and capital gains aren't subject to tax. Compound interest is used in savings accounts, money market funds, bond funds, personal loans, auto loans, mortgages, credit cards, and other financial products.

## Why is compound interest so powerful?

Compound interest is a highly effective tool for accelerating the growth of a savings or investment portfolio over the long run. The reason is that the interest earned is based on the original principal and the accumulated interest from prior periods. Since interest is continuously applied to the principal, the returns grow exponentially. As a result, it enables investors to amass vast sums of money with modest initial investments.

## Contributors

### Mark Gregorski

Mark is passionate about educating people on how the financial markets work and providing tips to help them better manage their money. Mark holds a bachelor’s degree in finance from the Northern Alberta Institute of Technology and has more than a decade of experience as an accountant.

Outside of writing and finance, he enjoys playing poker, going to the gym, composing music, and learning about digital marketing.