Simple vs. Compound Interest
Introduction
What happens when we borrow or invest using simple or compound interest?
Is one type of interest better than the other?
Let’s get into it!
What is interest?
Definition
Interest
The term interest refers to both the money earned when you save or invest money, as well as the money or fees paid when you borrow money from a bank or other institution.
When someone puts money into a tax-free savings account or other investment, they may earn interest on top of their initial or principal investment.
If someone is borrowing money from a financial institution, they will likely need to pay interest on the amount borrowed or their balance.
The amount of interest is based on an interest rate. An interest rate is usually in the form of a percentage and shows how much is earned in addition to the initial amount, or how much the lender charges on top of the initial amount.
So, when someone is thinking about investing or borrowing, it is important to understand the type of interest attached and the interest rate.
Understanding simple and compound interest
Usually, the type of interest we will see attached to investments and credit is simple or compound interest.
Notebook
Access the video titled “Run the Numbers: Simple vs. Compound Interest” to better understand the difference between simple and compound interest.
After watching the video, record the main difference between simple and compound interest in your notebook.
Press the show answer button to compare your answer.
Simple interest is interest applied to the principal amount. Whether you are investing or borrowing, simple interest will grow on the principal amount only.
For example, in the video, simple interest is earned at a rate of 50% daily. Therefore, the investor would earn half a fry every day in interest, and the principal would stay the same.
A plate labeled “Principal” containing one French fry is next to an empty plate labeled “simple interest”. After earning 50% simple interest each day for five days, the second plate holds five half fries, and the first plate continues to hold one fry.
A plate labeled “Principal” contains one fry, while an empty plate is labeled “simple interest”. After earning 50% simple interest each day for five days, the second plate holds five half fries and the first plate continues to hold one fry. Paragraph locked by Jacquie Busby
Compound interest is interest that is applied to the principal amount as well as the interest that accumulates along the way. For example, in the video, the compounding frequency, or the number of times the principal + interest is reinvested, is daily with an interest rate of 50%. This means that each day the principal amount is growing by 50%. A the end of day one, the principal would grow from one fry to one and a half fries.
A plate labeled “principal” containing one French fry is beside an empty plate labeled “compound interest”. After earning 50% compound interest in one day, the “Principal” plate holds one and a half fries and the “compound interest” plate is empty.
Note: In the video, Sean gives the example of an interest rate that is compounded at 50% daily. Usually, compounding frequencies occur monthly, or annually.
Simple interest
Simple interest is calculated using a formula that considers the initial amount borrowed or invested (the principal), the rate, and the length of time the money is borrowed.
Simple interest formula
A = P(1 + rt)
A = final amount
P = initial principal balance
r = annual interest rate
t = time (in years)
Gabby: So, if someone decides to put $500 into a tax-free savings account and the annual interest rate is 4%, how much interest would they earn after four years?
Clara: We would need to convert the percentage to a decimal form first, so 0.04. Now, let’s add everything into our formula for simple interest.
If we round to the nearest thousandth, this is what our result looks like!
A = P(1 + rt)
A = 500 (1 + 0.04 x 4)
A = 500 (1 + 0.16)
A = 500 (1.16)
A = 580
So, the interest they would earn after four years is $80.
Compound interest
Compound interest is calculated using a formula that considers the initial amount borrowed or invested, the rate, the length of time the money is borrowed, and the number of times per year that the interest is compounded.
This means that every year, the interest that is earned is added back into the principal and then reinvested.
Compound interest formula
A = P(1 + )t
A = final amount
P = initial principal balance
i = interest rate as a decimal
n = number of compounding periods per unit of time
t = total number of compounding periods in the investment
Gabby: So, then let’s say someone decides to put $500 into a tax-free savings account that is compounded at 4% interest twice a year. How much would the principal grow over the course of four years?
Clara: Let’s add everything into our formula for compound interest and find out!
The number of times that the interest is compounded is twice a year. That means that in four years, it will have compounded eight times.
If we round to the nearest thousandth, this is what our result looks like!
A = P(1 + )t
A = 500(1 + )8
A = 500(1 + 0.02)8
A = 500(1.02)8
A = 500(1.17)
A = 585
The interest they would earn after four years is $85.
The interest they would earn after four years is $85. The account that used compound interest gained $5 more after a four-year period.
Compound interest can help your money grow faster. At the beginning of an investment, there is less gain, but with time, compound interest accelerates in growth. It’s also important to consider the interest rate and compounding frequency.
What do you think would happen if the account was compounded three times a year, at 15% for a 20-year period?
Getting advice before you save or invest
When setting up a savings account or an investment, it is helpful to consult a financial planner. They can provide information and advice about the following:
- the interest rates that are available (e.g., 1%, 1.5%, 5% etc.)
- the type of interest attached (simple vs. compound)
- any fees attached (e.g., monthly withdrawal fee or annual fee)
- the principal amount to be saved or invested
- the time frame
Everyone’s financial situation looks different at different times in their lives. It is always important to take the time to get advice, research your options, and take the time to make the decision that works best for you!
Let’s reflect
We have discussed simple and compound interest when it comes to savings and investments. However, simple and compound interest can also be applied to borrowing money (credit).
What factors might someone consider when choosing between different borrowing or credit options? Consider the type of interest rate, amount, and time period.
Do you think that one type of interest is better than the other? Why or why not?
Record your thoughts and share with a partner if possible.
Self check
Next, check your understanding with the following multiple-choice questions. Select the correct answer, then press the Check Answer button to see how you did.
Gabby’s savings plan
Gabby’s mom has offered to open a tax-free savings account for Gabby that she will manage until Gabby graduates from high school.
To start, Gabby has saved $100 that she would like to put into the savings account.
There are three options that Gabby and her mom can choose from:
Option 1: A tax-free savings account with an annual interest rate of 5% and a monthly fee of $3. This means that every month, they would have to pay $3.
Option 2: A tax-free savings account with an interest rate of 2% compounded four times a year with monthly fee of $2. This means that every month, they would have to pay $2.
Option 3: A tax-free savings account with an interest rate of 3% compounded twice a year with no monthly fee.
Which option do you think will help Gabby save the most money? You may do your calculations using the interest formulas provided or an online interest calculator of your choice. Record your thoughts and share with a partner if possible.
Press the Hint button for help.
Remember that the term compounded tells us that compound interest is being applied.
Simple interest formula
A = P(1 + rt)
A = final amount
P = initial principal balance
r = annual interest rate
t = time (in years)
Compound interest formula
A = P(1 + )t
A = final amount
P = initial principal balance
i = interest rate as a decimal
n = number of compounding periods per unit of time
t = total number of compounding periods in the investment