# The magic of compound interest

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Updated: August 10, 2023

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Compound interest is a powerful tool that can pave your way to a luxurious retirement or lead you into financial ruin. Here’s what compound interest is, an explanation of simple vs. compound interest, and instructions for using the compound interest formula and our compound interest calculator.

Compound interest is an aspect of personal finance that’s so potent. It has the power to swell your savings into a substantial retirement nest egg or leave you in an ever-expanding hole of debt. What is this financial phenomenon and how can you use it to your advantage? We’ll explain it all below with a definition of compound interest (and how it differs from simple interest), a formula for determining compound interest amounts, and a handy compound-interest calculator to crunch the numbers and help you make informed financial decisions.

## What is compound interest?

In short, compound interest is interest that continues to build upon itself.

So, for example, if you earn 5% annual interest on an initial deposit of \$100, by the end of the first year you’d get \$5 in interest and your total account balance would rise to \$105. By the end of the second year, you’d earn slightly more in interest income—\$5.25—because the 5% interest is calculated on the total sum of \$105, rather than your initial deposit of \$100. Similarly, by the end of year three, you’d earn \$5.51 in interest income or 5% of the total \$110.25 in your account.

In other words, compound interest means the interest rate is applied to your full balance, including any amounts you previously earned in interest.

These growing increments of interest income can make a huge difference to your total savings over time. In fact, with an interest rate of 5%, you’d more than double your money in 15 years just by letting your initial deposit earn compound interest year after year. And, while doubling an initial deposit of \$100 to about \$208 over a 15-year period may not sound like a path to riches, consider this: if your initial deposit had a few more zeros at the end, \$10,000 becomes \$20,789; and \$100,000 becomes \$207,890.

## Simple vs. compound interest

Simple interest is calculated and paid only on your principal investment (as well as on any new deposits you happen to make). With simple interest, you won’t earn interest on any of the previous interest payments you received, so your savings won’t grow as quickly as they would with compound interest.

In our example above, you’d earn \$5 of interest every year on an initial deposit of \$100, and it would take you 20 years—more than five additional years—to double your money.

## Compound interest formula

If you wanted to figure out how much you would earn in compound interest on a particular sum of money, you could use the following formula:

Compound interest = P [(1 + i)n – 1]

P = principal amount (initial investment)

i = annual nominal interest rate

n = number of compounding periods

Here’s a real-life example of how you would use the formula. Say you purchased a \$10,000 3-year GIC (guaranteed investment certificate) from an online bank at an annual rate of 2.50%. Your principal amount invested (P) is \$10,000, the annual nominal interest rate (i) is 0.025, and the number of compounding periods (n) is 3.

Here’s how the formula looks with your numbers plugged in:

Compound interest = \$10,000 [(1 + 0.025)3 – 1]

= \$10,000 [1.076890625 – 1]

= \$10,000 x 0.076890625

= \$768.91
The total amount of compound interest you would earn over the three-year period on your \$10,000 GIC is \$768.91.

## Compound interest calculator

Take a moment to fill in the amounts from our GIC example above in the compound interest calculator: \$10,000 initial investment, 2.5% interest rate, interest calculated annually, and 3 years to grow. Click calculate and – voilà! – the total interest earned is displayed as \$768.91—the same result as using the formula.

As an added bonus, the calculator also allows you to see how depositing even small amounts to your savings on a regular basis can boost the power of compounding.

And you can even use it to compare various financial products since it lets you easily assess how various interest rates, compounding intervals, and the number of years an asset or debt is held will impact your final balance.

## Compounding and investments

In the same way that interest income builds on itself over time to your advantage, investment earnings can do the same—but on an even larger scale. That’s because investments can earn a much higher rate of return than interest. And, if those investments are held within a registered account—such as an RRSP or TFSA, where earnings can be left to compound tax-free for decades—the growth can be exponential.

Let’s use the compound interest calculator to illustrate. Say you decided to invest \$15,000 in a TFSA or RRSP account that provided average annual returns of 6% per year, and you set up automatic monthly contributions of \$100. Plug in the amounts to the calculator to get results after 5, 15, 25 and 35 years, as follows:

Day 1
After 5 years
After 15 years
After 25 years
After 35 years
Deposits
\$15,000
\$21,000
\$33,000
\$45,000
\$57,000
Investment earnings
N/A
\$6,050
\$32,030
\$88,677
\$200,762
Balance
\$15,000
\$27,050
\$65,030
\$133,677
\$257,762

With a relatively small initial investment, very reasonable monthly deposits and a modest rate of average annual investment returns, you would more than quadruple your money in 35 years—turning deposits of \$57,000 into a total nest egg of \$257,762. To be more precise, that’s a 452% return on investment. That is the power of compounding.

To make sure you don’t lose any of those investment returns to high fees, use a low-fee online brokerage if you prefer to do your own investing. Our top pick is Questrade, where you can purchase ETFs for free through their self-directed platform. Plus, if you sign up for Questrade, you’ll get \$50 in free trades via our exclusive link when you fund your account with \$1,000 as a welcome bonus.

We’re also big fans of Wealthsimple Trade – Canada’s first and only zero-commission trading platform. If you’re comfortable with a mobile-only platform, you can open an account and trade stocks and ETFs for free. Plus, you can take advantage of our exclusive promo offer: open a new Wealthsimple Trade account, and get a \$25 cash bonus + \$0 commission trades. All you have to do is fund at least \$150.

If you’d rather delegate the work of managing your investment portfolio, consider a robo advisor. These platforms offer low-fee ETF portfolios and other cost-effective investments to meet the needs of both first-time and experienced investors.

There are plenty of excellent robo advisors in Canada, but our favourite is Wealthsimple Invest. Its intuitive, sleek platform combined with competitive fees and premium perks make Wealthsimple a winner. Here’s another excellent reason to sign-up: those who open and fund their first Wealthsimple account with min. \$500 will get a \$25 cash bonus. Plus, Wealthsimple Trade will reimburse an outgoing administrative transfer fee of up to \$150 on investment account transfers valued at more than \$5,000.

## Compound interest and debt

Until now, we’ve only discussed the benefits of compound interest—and how it can help grow your savings more quickly over time.

But compound interest can also work against you. When you take on debt, especially high-interest debt, compound interest may mean paying far more in interest charges than you realize. The average credit card interest rate in Canada, for example, is about 19% APR. But, once you figure monthly compounding into the equation, the actual amount of interest paid on any outstanding balances can far exceed 19%.

Here’s how it works. Each month, one-twelfth of the annual interest rate (or 1.58%, in the case of a 19% APR) is applied to the remaining balance on your credit card. The next month, another twelfth (1.58%) is applied to your balance, which (unless you’ve paid it off) now also includes the interest charges from last month. The credit card company is charging you interest on your previous interest charges!

In the end, this means you will typically pay a higher percentage of your original loan than the advertised annual percentage rate (APR) since the interest is charged on a monthly (rather than annual) basis. This makes it harder to chip away at the principal amount you’ve borrowed and it’s the reason why so many people can find it overwhelming to get out of debt.

Conversely, if you use a low-interest rate credit card—and pay off your debt quickly—the interest charges can’t compound as much. As a result, you will pay significantly less in interest than if you spent years making the minimum payments on a higher-rate card. These credit cards are also ideal when you carry a balance or new to finance a new purchase at a more attractive interest rate. Some credit cards offer low-interest rates just for a promotional period only (for example, six months). Others may charge an annual fee to take advantage of their low-interest rates. The good news is that you will be less negatively impacted by compound interest rates on unpaid balances. It’s one smart strategy to avoid paying credit card fees.

## Final thoughts

Timing is clearly one of the most important aspects of compounding, which is why investment accounts are highly recommended for young people. Start leveraging the power of compound interest and compound investment income now, so you don’t squander the opportunity to see your savings grow. It’s why you should start investing as early as possible. For your everyday banking, make sure that you choose a bank that offers a decent interest rate.

On the flip side, be wary of the negative impact of compound interest on debts. It can escalate a moderate credit card balance into something that is more difficult to pay off. If you have credit card debt, consider some smart ways to pay off the balance pronto. Make compound interest work for you by focusing on its ability to supercharge your savings over time.

Tamar Satov Freelance Contributor

Tamar Satov is an award-winning journalist specializing in the areas of personal finance and parenting. Her work has appeared in Canadian Living, The Globe and Mail, Today’s Parent, Parents Canada, Walmart Live Better and many other consumer magazines and websites.

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