An Introduction To Compound Interest

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Compound interest has long been one of the most important concepts in investing–it’s when you earn interest upon an amount that’s already earned interest. Over time, the continual compounding of “interest on interest” on top of your original contribution creates a snowball effect, which enables your money to grow at a faster and faster rate.

It’s partly for this reason why investments experts say to save early–the earlier you start the more time your money has to compound, which, depending on your rate of return, time horizon and goals, could add thousands of dollars towards your savings goals.

What is compound interest?

First, it’s important to understand how interest works. Take a savings account. If you keep money in an account at a bank, the bank will pay you interest on that deposit for keeping that cash at their institution. The interest rate it pays is usually calculated and paid out on a monthly, quarterly or annual basis. If a savings account comes with a 2% interest rate that’s paid out annually, a $1,000 deposit will earn you $20 in interest at the end of the year.

With investing, the rate depends on your investment. Fixed-income investments such as bonds or guaranteed investment certificates (GICs) promise a certain rate of return after a specific period of time. Stocks, exchange traded funds (ETFs) and mutual funds may pay out dividends, but the rate of return isn’t guaranteed and it depends on how the underlying investments perform.

If the markets are rising, then compounding can begin right after you make your first deposit. If you invest $10,000 in an ETF and, over the year, that fund rises in value by 2% then you now have $10,200. If it rises by another 2% over the next year, you’ll have $10,404. Because the growth in year two is based on $10,200–the principal plus the $200 in interest–you get an extra $4 thanks to compounding. The more money you invest, the more that will compound over time. (We look at how compounding works in more detail below.)

Compound interest can also work against you, especially when it comes to personal debt, such as credit cards, loans and mortgages. If you don’t pay off your credit card in full every month or make on-time payments according to the terms of your loan, interest will compound on top of the amount you already owe. As well, if a stock you own falls for a couple of years in a row, that loss will be worse thanks to compounding–it worse in reverse in a down market-which means you’ll have to earn more to break even.

Savings accounts in Canada typically offer interest rates between 1% and 3%, with interest calculated daily and paid monthly. Savings accounts are useful for short-term savings and things like emergency funds when you need to easily access cash, but they won’t cut it for long-term growth. To earn higher returns and combat inflation, you need to invest.

How does compound interest work?

There are a few variables that go into calculating compound interest, including how long you have to invest, the interest rate and how often it compounds, and any additional contributions on top of the principal amount.

Time horizon

In general, having more time on your side makes a big difference for saving and investing. For compounding to do its work it needs time–to earn interest and then earn more interest. While you can start saving and investing at any age, the reality is that someone in their early 20s will benefit more from compounding than someone who only started to invest in their 40s.

Compounding frequency

Interest can be accumulated daily, weekly, quarterly, or annually. The more often interest compounds, the faster your balance grows. Interest can also be compounded on one frequency but distributed on another. For example, a savings account may calculate interest daily but pay it out monthly.

Interest rates

A higher interest rate means a higher rate of return on your investment. Your return also depends on whether or not your investments are guaranteed or non-guaranteed. Savings accounts have lower interest rates, and banks have the discretion to change them at any time. For non-guaranteed investments such as stocks, ETFs or mutual funds, it depends on how the markets perform.

Additional contributions

How much you continue to contribute to your savings, and how often, will also determine how quickly your savings accumulate. Saving $25 or $50 at a time might not seem like a lot, but regularly putting away small amounts of money over a long period of time can really add up thanks to compounding.

Simple interest vs. compound interest

Simple interest refers to interest that doesn’t compound. It’s only paid on the principal amount, and doesn’t add any accumulated interest to the balance for reinvestment. Simple interest works more in your favour if you’re borrowing money, because you’ll pay a lower amount in interest charges. If you’re investing money, you want your interest to compound to bolster your balance.

Simple interest is used to calculate fixed-term investments such as bonds or GICs. As its name suggests, it’s easy to use the simple interest formula: P x r x n.

P = Principal amount
r = Annual interest rate
n = Term of loan, in years

Let’s say you deposit $5,000 in a GIC that pays 5% over a two-year term. 5000 x 0.05 x 2 = 500. You’ll earn a total of $500 in interest, or $250 per year. Even though it’s a two-year term, the interest only accumulates on the principal amount—the $250 earned in the first year isn’t added to the principal for reinvestment in the second year.

How to calculate compound interest

Calculating compound interest is a little more complicated than simple interest, but you can do it using the standard compound interest formula: A = P (1 + [ r / n ]) ^ nt

A = Accrued amount
P = Principal amount invested
r = Annual interest rate (in decimal format)
n = Number of compounding periods per year
t = Number of years to grow (use decimal format for months)

Here’s an example of how to calculate compound interest on an original investment of $1,000 over a period of 10 years, with an annual interest rate of 5% that compounds monthly.

Principal amount invested (P) = $1,000
Annual interest rate (r) = 0.05
Compounding periods (n) = 12
Years to grow (t) = 10 years

You’ll need a calculator with an exponent function for steps 2-3, or, better yet, use an online compounding interest calculator. If you want to do it the old fashioned way, grab a pen and paper and do this:

1. A = P (1 + [ r / n ]) ^ nt
2. A = 1000 (1 + [0.05 / 12]) ^ (12 x 10)
3. A = 1000 (1.00417) ^ (120)
4. A = 1000 (1.64767)
5. A = 1,647.67

After 10 years, your initial deposit of $1,000 would grow to about $1,647. That means you’ll earn $647 in interest.

Rule of 72

For a less complicated calculation, which you can easily do in your head, use the rule of 72. It’s a way to estimate how long it will take to double your investment, assuming a fixed annual interest rate. It isn’t exact, but it works best for interest rates around 5% to 15%.

To find the number of years required to double your money, simply divide 72 by the interest rate. For example, if you want to know how long it will take to double your initial investment with an 8% interest rate dividend 72 by eight, which equals nine. It will take nine years to double your investment.

There are a few variations on the rule of 72, depending on the interest rate and how often it compounds. An interest rate of 8% is considered the sweet spot for the rule of 72, but you can also adjust it by one point for every three points the interest rate moves away from 8%. So if the interest rate is 5%, it would become the rule of 71.

For interest that compounds daily instead of yearly, the (less catchy) rule of 69.3 is considered more accurate. If you’re really ambitious, you can use the rule of 114 to calculate how long it will take your investment to triple.

Compound interest calculators

Don’t worry if math isn’t your strong suit—it’s the 21st century, and there are a lot of online compound interest calculators out there to do the work for you.

It’s useful to understand the mechanics behind how compound interest is calculated, but using an online interest calculator comes in handy when you want to factor in ongoing contributions over a long period of time. All you have to do is plug in a few numbers:

• Principal amount
• Additional contributions (bi-weekly, monthly, quarterly, annually, etc.)
• Interest rate
• Interest compounding frequency (monthly, quarterly, annually, etc.)
• Number of years to grow

You can find compound interest calculators through a quick search online, or check out this user-friendly one from the Ontario Securities Commission.

Understanding how compound interest is calculated is a simple way to estimate how much your savings will be worth in the future, and gives you a clearer idea of how much you need to save—and at what rate—to meet your future goals. If you start saving and investing ASAP, contribute consistently and have a little patience, compounding can generate significant savings over time.