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F1.5 · Explain how interest affects saving, investment, and borrowing

Learn to explain how interest affects saving, investment, and borrowing through clear examples and targeted practice.

Ontario Grade 7 Mathematics

Financial Literacy

A Grade 7 lesson about money earned or paid over time

Imagine saving CAD 100 for one year. In one example, the money earns no interest. In another, it earns interest. Interest is money earned or paid for the use of money over time. It can add to savings or to some investments. It can also add to the cost of borrowing. This lesson uses hypothetical examples, meaning the amounts and terms are made up for learning. They are not financial offers.

What you will learn

Explain what interest is and who earns or pays it.
Describe how interest can affect saving, investing, and borrowing.
Use a simple model to find and compare interest amounts.

What interest means

Before working with interest, recall two ideas. An amount is a quantity of money. A percent means a number of parts out of 100. For example, 4% means 4 parts out of 100. So 4% of CAD 100 is CAD 4.

The starting amount is often called the principal. In this lesson, principal means the amount first saved, invested, or borrowed. An interest rate tells what percent of the principal is earned or owed during a stated time. Always notice the time period: a rate for one year is not the same statement as a rate for one month.

For a simple model, find the stated percent of the principal for each stated year, then multiply by the number of years. Let

I

mean interest,

P

mean the principal,

r

mean the yearly rate written as a decimal, and

t

mean the number of years. To write a percent as a decimal, divide it by 100. For instance, 4% is 0.04. This model assumes the same interest is calculated from the starting amount each year. It is useful for these clear examples, but real arrangements can use different rules.

If a problem gives a rate for one year and asks about one year, then

t=1

. If it asks about two years under this model, then

t=2

. The model helps explain how the amount, rate, and time affect interest. It does not tell us that every account or investment uses these terms.

I=P\times r\times t

Interest is money earned or paid for the use of money over time.
The principal is the starting amount.
A rate needs a time period, and the model uses a decimal rate and a stated number of years.

Saving and investing

Saving means keeping money for later instead of spending it now. A savings account may pay interest. If it does, the saver receives money in addition to the amount saved. For example, a hypothetical 4% yearly rate on CAD 300 gives CAD 12 interest for one year. The simple total is the CAD 300 starting amount plus CAD 12.

An investment is money used with the aim of future growth or another future benefit. Some investments may pay interest. In that case, interest is one possible return: money received because the money was invested. Do not assume that every investment pays interest or that every investment grows. The result depends on its stated terms.

When comparing two examples, keep track of the principal and time as well as the rate. If the principal and time are the same, a higher rate gives more interest in this simple model. If the rate is the same, a larger principal gives more interest. More time also gives more interest in this model when the rate stays the same. These comparisons describe the model, not a promise about an actual account or investment.

A bar chart can make the parts of a total easier to see. The interest bar represents the extra amount earned; the starting amount remains separate. Add the two amounts only when the question asks for the simple total.

A saver may receive interest, which can add to savings.
Some investments may pay interest, but investment results depend on their terms.
Compare the principal, rate, and time together.

Borrowing

Borrowing means using money that must be repaid under stated terms. A borrower receives the money. A lender provides it. Interest is usually an added cost for the borrower and money received by the lender.

For a simple one-year example, borrowing CAD 600 at a hypothetical yearly rate of 3% gives CAD 18 interest. The borrower must account for the borrowed amount and the interest. The simple total is CAD 618. The interest is not the amount borrowed; it is an extra cost connected with borrowing.

A higher rate can mean more interest to pay when the principal and time are kept the same. A different principal or a different length of time can also change the interest. So a rate on its own does not tell the full story. To understand the effect, check the amount borrowed, the rate, the time, and the stated terms.

Interest has different effects on the two sides of borrowing. It costs the borrower and is received by the lender. Before deciding whether interest helps or costs someone, ask who receives it and who pays it.

simple total to repay=amount borrowed+interest

A borrower usually pays interest to a lender.
Interest adds to the cost of borrowing.
The simple total is the amount borrowed plus the interest.

A useful way to reason about interest

First identify the situation: saving, investing, or borrowing. Next identify who receives interest and who pays it. Then check the principal, the rate, and the time period. Finally, decide whether the question asks for the interest alone or for a total that includes the starting amount.

When the rate is written as a percent, you can find the percent by finding 1% first. Since 1% is one hundredth of an amount, divide the principal by 100. Then multiply that result by the number of percent parts. For example, to find 3% of CAD 600, find 1% and take three equal groups. This is the same reasoning as using a decimal rate in the formula.

Try this before looking at the examples: a hypothetical saver puts away CAD 500 for one year at 2%. Is interest earned or paid? What is 1% of CAD 500? Then find 2%. The saver earns CAD 10 in this model. For borrowing, the same calculation would describe interest paid by the borrower instead.

Name the situation and identify who receives or pays interest.
Check the amount, rate, and time before comparing.
Separate interest from the starting amount when finding a total.

How interest can affect each situation

Situation	Possible effect of interest
Saving	The saver may earn interest, adding to savings.
Investing	Some investments may provide interest as a return.
Borrowing	The borrower usually pays interest, adding to the cost.

Worked example

A saver earns interest

A hypothetical savings account pays 4% for one year. How much interest is earned on CAD 300, and what is the simple total after that year?

Hypothetical savings and interest

The bars show the stated starting amount and the interest earned in the one-year example.

Find 4% of the starting amount
Since 4% is four groups of 1%, first find 1% of CAD 300 by dividing by 100. Then take four groups of that amount.
$300\div100=3,\quad 3\times4=12$
Add interest to the savings
The simple total includes the original CAD 300 and the CAD 12 earned as interest.
$300+12=312$

Answer: The interest is CAD 12. The simple total after one year is CAD 312.

Check: Four groups of CAD 3 equal CAD 12, so the interest is less than the CAD 300 starting amount and the total is CAD 312.

Worked example

Compare two hypothetical investment rates

Two hypothetical investments each use CAD 400 for one year. One pays 2% interest and the other pays 5%. How much interest does each pay, and how much more does the higher-rate example pay?

Interest from two hypothetical investments

The bars compare interest only. Both examples use CAD 400 for one year.

Find the interest at 2%
Find 1% of CAD 400, then take two equal groups.
$400\div100=4,\quad 4\times2=8$
Find the interest at 5%
The principal and time are unchanged. Take five groups of the same 1% amount.
$4\times5=20$
Compare the interest amounts
Subtract the smaller interest amount from the larger one to find the difference.
$20-8=12$

Answer: The 2% example pays CAD 8 in interest. The 5% example pays CAD 20, which is CAD 12 more.

Check: Both examples use the same principal and time, so the higher rate gives more interest in this model.

Worked example

Interest adds to borrowing cost

A person borrows CAD 600 under a hypothetical one-year arrangement with 3% interest. How much interest is owed for that year, and what is the simple total to repay?

Hypothetical borrowing amount and interest

The bars separate the CAD 600 borrowed from the CAD 18 interest cost for one year.

Find 3% of the borrowed amount
Find 1% of CAD 600 by dividing by 100. Then take three equal groups.
$600\div100=6,\quad 6\times3=18$
Add interest to the amount borrowed
In this simple example, the total includes the CAD 600 borrowed and the CAD 18 interest cost.
$600+18=618$

Answer: The interest is CAD 18. The simple total to repay is CAD 618.

Check: Interest is an added borrowing cost, so the simple total is greater than CAD 600.

Common mistakes and how to avoid them

Thinking interest always helps the person whose money is involved.

Correction: Interest can help a saver or investor who receives it. It usually costs a borrower who pays it.

Comparing interest rates without checking the principal or time.

Correction: To see the effect of the rate alone, keep the principal and time the same.

Assuming all investments earn interest or are guaranteed to grow.

Correction: Some investments may pay interest, but results depend on their terms. A hypothetical example is not a promise.

Giving the total amount when asked for interest alone.

Correction: Interest is the earned or owed amount. Add it to the starting amount only when the question asks for a total.

Lesson summary

Interest is money earned or paid for the use of money over time.
A saver or investor may receive interest, which can add to money held or invested.
A borrower usually pays interest, which adds to the cost of borrowing.
In the simple model, interest depends on the principal, decimal rate, and stated time.
Always check who receives interest, who pays it, and whether the question asks for interest or a total.

Check your understanding

Question 1

In a hypothetical one-year example, a person saves CAD 200 at 3% interest. How much interest is earned?

CAD 3
CAD 6
CAD 20
CAD 203

Show answer and explanation

CAD 6

One percent of CAD 200 is CAD 2. Three groups of CAD 2 give CAD 6.

Question 2

A borrower pays interest on money borrowed. What is the usual effect of that interest?

It reduces the amount borrowed.
It adds to the cost of borrowing.
It is always paid to the borrower.
It makes the borrowed amount disappear.

Show answer and explanation

It adds to the cost of borrowing.

Interest is usually an extra cost for the borrower and money received by the lender.

Question 3

Two hypothetical savings examples have the same principal and time. One has a higher interest rate. What can you conclude in the simple model?

The higher rate gives less interest.
Both must earn exactly the same interest.
The higher rate gives more interest.
The principal must be different.

Show answer and explanation

The higher rate gives more interest.

When the principal and time are the same, a higher rate gives more interest in this model.

Key terms

Interest: Money earned or paid for the use of money over time.
Principal: The starting amount saved, invested, or borrowed.
Interest rate: The percent used to describe interest for a stated time.
Borrower: A person who receives borrowed money and must repay it under the stated terms.
Lender: A person or organization that provides money to be borrowed.
Investment: Money used with the aim of future growth or another future benefit.
Return: Money or another benefit received from an investment.

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Published by DoAssignment. This reviewed lesson follows Ontario Grade 7 Mathematics, expectation F1.5. It is a study resource, not an official curriculum publication.

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