Simple vs compound interest: What’s the difference?

Navigating the financial implications of simple and compound interest is invaluable for anyone managing personal finances. This article dives into the fundamental differences between these two types of interest to provide you with the knowledge needed to make well-informed decisions about your investment, borrowing and savings options.

What is the difference between simple and compound interest?

Simple and compound interest are two fundamental methods for calculating interest on money that is either borrowed or invested.

Simple interest is calculated directly on the principal amount, which is the original sum of money at the start of the investment or loan.

This method applies a fixed rate over the term, making it straightforward and predictable for calculating total interest over time.

Compound interest involves a more dynamic approach where interest is calculated not only on the principal but also on any interest that has already accumulated. Unlike simple interest, compound interest grows incrementally because each period’s interest is added back to the principal, forming a new base for the next calculation period.

This method results in faster investment growth over time, offering greater returns on investments and, conversely, potentially higher costs on debts if not managed carefully.

Understanding these differences is crucial for anyone looking to invest wisely or manage debt efficiently, as each type of interest calculation method significantly impacts financial outcomes over time.

Summary: Difference between simple and compound interest

	Simple interest	Compound interest
Definition	Interest is calculated only on the original principal amount, resulting in a fixed growth rate over time.	Interest is calculated on the original principal plus any accumulated interest, leading to exponential growth over time.
Formula	Principal amount × interest × loan term	P(1 + r/n)nt
Savings accounts	✘	✔
Chequing accounts	✘	✔
Car loans	✔	✘
Personal loans	✔	✔
Lines of credit	✔	✘
Credit cards	✘	✔
GICs	✔	✔

What is simple interest?

Simple interest is a straightforward method for calculating the interest you earn or pay on a loan or investment based solely on the original amount, known as the principal.

This type of interest is straightforward because it does not compound; in other words, interest is not earned on top of previously earned interest.

Simple interest is generally used in specific types of loans, such as some auto loans, student loans and short-term personal loans, where it is calculated on the principal amount owed. It can also apply to certain financial instruments like bonds, where fixed interest payments are made on the face value.

Overall, simple interest offers benefits in situations where simplicity and predictability are more desirable than the potentially higher returns of compound interest.

Simple interest formula

Simple interest is determined by multiplying the principal by the interest rate and the time period over which the interest is accrued.

The formula to calculate simple interest is straightforward:

A = P(1+ rt)

Where:

• P is the principal amount (the initial sum of money)
• r is the annual interest rate (in decimal form)
• t is the time the money is borrowed or invested (in years)

Example of using the simple interest formula

Imagine you take out a loan of $5,000 with a simple interest rate of 6% per year. You plan to repay this loan over a period of three years. Using the simple interest formula, you can calculate the interest you will owe as follows:

P = $5,000
r = 6% or 0.060 as a decimal
t = 3 years

Plugging these values into the formula, you get:

A = $5,000 (1 + (0.06 × 3))
A = $5,900

Therefore, over three years, you will pay a total of $900 in interest. This means, by the end of the loan term, you will have paid back a total of $5,900.

What is compound interest?

Compound interest is a financial concept used in both savings and borrowing where interest is calculated on the initial principal as well as the interest accumulated from previous periods. This means that each interest calculation builds upon the last, adding interest to the interest that has already accrued.

For investments, this leads to exponential growth over time, as the earnings are continually reinvested to generate more earnings.

For loans, compound interest increases the debt more quickly than simple interest because each calculation adds to the principal amount owed, potentially making the debt grow faster and larger if not managed carefully.

Essentially, compound interest magnifies the effect of interest over time, benefiting savers and investors with increased returns, while posing a higher cost to borrowers.

Compound interest formula

The formula for calculating compound interest is expressed as:

A = P (1 + r/n)^nt

Where:

• P is the principal amount (the initial sum of money)
• r is the annual interest rate (expressed as a decimal)
• n is the number of times interest is applied (per unit of time)
• t is the time the money is borrowed or invested (in years)

Now calculate:

A = $3,000 (1 + 0.025/1) ^{(1 × 5)}

Example of using the compound interest formula

Imagine you invest $3,000 in a Guaranteed Investment Certificate (GIC) that offers an annual compound interest rate of 2.5% compounded annually. You plan to keep this investment for five years. Using the compound interest formula, you can calculate how much money you’ll have at the end of this period.

Plugging the values into the formula:

• P = $3,000
• r = 0.025 (2.5% expressed as a decimal)
• n = 1 (compounded annually)
• t = 5 (money is invested for 5 years)

Now calculate:

A = $3,000 (1 + 0.025/1) ^{(1 × 5)}

At the end of five years, your initial investment of $3,000 in the GIC will have grown to approximately $3,394.23. This means you earned $394.23 in compound interest.

Simple vs compound interest on your savings

Simple interest is calculated on the principal alone and does not accumulate over time, making it less effective for long-term savings growth. For instance, $5,000 at a simple interest rate of 3% annually, yields $1,500 after 10 years totaling $6,500.

As mentioned previously, compound interest is calculated on both the principal and the accumulated interest, leading to exponential growth. The same $5,000 at a 3% rate compounded annually grows to about $6,718 over the same period.

As you can see, compound interest significantly increases savings, especially as the compounding frequency increases over time.

For optimal long-term savings, its advisable to prioritize financial products that offer compound interest like TFSAs or RRSPs, which provide the added benefit of tax advantages, and high interest savings accounts. Understanding the type of interest applied on your savings account helps you maximize your savings potential.

Dive deeper: Our guide to savings account interest rates in Canada

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Simple vs compound interest on your debt

Debt with simple interest is calculated solely on the original loan balance, keeping costs predictable and easier to manage. This predictability can make it easier to manage payments, as the interest does not increase.

If you borrow $10,000 at a simple interest rate of 5% per year for five years, you’ll owe a total of $2,500 in interest, making the overall repayment $12,500.

In contrast, compound interest on debt can significantly increase the amount you owe because it is calculated on both the initial principal amount and the accumulated interest. If the same $10,000 is subjected to a 5% compound interest rate annually, the total interest grows to about $2,763 over five years and you would owe $12,763.

That compounding effect becomes more burdensome the longer the debt remains unpaid.

To minimize debt costs, it’s advisable to choose loans with simple interest if possible, especially for larger or longer-term debts. Understanding how interest compounds on your debt is crucial for effective debt management and can influence your overall financial health.

Dive deeper: Guide to personal loan interest rates in Canada

Simple vs compound interest on your investments

The type of interest applied to your investments can significantly affect their growth over time. Simple interest, which is rare in typical investment scenarios, calculates interest only on the original principal. This means the growth is linear and doesn’t accelerate over time.

For instance, if you invest $10,000 at a simple interest rate of 4% annually, you would earn $400 each year, irrespective of the investment duration.

Compound interest, more commonly used in investments, allows your earnings to grow exponentially, as interest is calculated on both the initial principal amount and the interest accumulated from previous periods.

For example, the same $10,000 at a 4% compound interest rate would not only earn interest on the principal but also on the interest earned in previous years. After 10 years (compounded annually) this would amount to approximately $14,802, compared to $14,000 from simple interest.

Investors looking to maximize their returns should opt for investments that offer compound interest, such as stocks, TFSAs and RRSPs. These investments benefit from the effect of interest on interest, significantly enhancing potential returns over longer periods.

Dive deeper: Our guide on the best stocks to invest in right now

Bottom line

Understanding simple and compound interest is crucial for effective financial management. This knowledge helps individuals choose the right loans to minimize costs and the best investment strategies to maximize returns. Being informed about how interest works allows for smarter financial decisions, directly impacting savings growth and debt management.

FAQs about simple vs compound interest

• Which is better: simple interest or compound interest?

  Compound interest is better for savings and investments compared to the same simple interest rate because it will help your money grow faster. On the other hand, simple interest is better for loans because you'll only pay interest on the principal, not the principal plus interest.

• Which is better for savings: 5% simple interest or 1% compound interest?

  A simple interest rate of 5% will yield a total of $2,500 in interest payments over 10 years (based on an initial deposit of $5,000), while a compound interest rate of 1% with the same initial deposit over the same length of time will yield a total of $525.62 in interest payments. Therefore, a simple interest rate of 5% is better than a compound rate of 1% on your savings, assuming all other factors remain the same.

• Are loans typically simple interest or compound interest?

  Most loans come with simple interest. However, certain types of debt like credit cards typically come with compound interest.