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F1.4 · Explain interest rates and fees for accounts and loans

Learn to explain interest rates and fees for accounts and loans through clear examples and targeted practice.

Ontario Grade 6 Mathematics

Financial Literacy

How accounts and loans can add to or take away from money

Suppose you put money into an account, or borrow money through a loan. The amount you save or borrow is not always the only amount that matters. An account may pay interest, charge fees, or do both. A loan may charge interest and fees. In this lesson, we will explain what those words mean and use clearly labelled hypothetical examples. A hypothetical example is made up for learning; it is not a real financial offer.

What you will learn

  • Explain what an interest rate tells you.
  • Describe how interest affects money in an account and money owed on a loan.
  • Explain how fees can change the total cost of using an account or loan.
  • Use stated information to compare interest and fees.

Start with the words

The amount of money you first put into an account is the starting amount. For a loan, it is the amount borrowed. A rate compares one amount with another. An interest rate tells what part of an amount is added as interest for a stated time.
Interest is money connected to saving or borrowing. An account may pay you interest for keeping money there. A loan may charge you interest for borrowing money. The words “pays interest” and “charges interest” describe different effects: one can add money to your account, while the other can add to what you owe.
A percent means “out of 100.” For example, 4%means means 4 out of every 100100. You can find 4% of CAD 100 by thinking of four groups of CAD 1. That amount is CAD 4. This review of percent helps us make sense of a stated interest rate.
A fee is a charge for a service or for using an account or loan. A fee may be a set amount, such as CAD 3 each month. The fee is separate from interest. When you compare choices, look for both.
  • Interest rates need a stated time period, such as per year.
  • Interest can be paid to an account or charged on a loan.
  • A fee is a charge and is not the same as interest.

Read the rate and the time

A rate by itself does not tell the whole story. Read the number, the time period, and what the rate applies to. An annual interest rate is a rate for one year. If a problem says an amount earns or is charged a rate for one year, use that stated time. Do not assume a different time period.
For a one-year example, you can find the interest by finding the stated percent of the starting amount. If CAD 100 earns 4% interest for one year, the interest is CAD 4. The account amount becomes CAD 104 if there are no fees or other changes.
The same idea helps describe a loan. If a loan charges 5% on CAD 200 for one year, the interest for that stated example is CAD 10. If no payments or fees are included in the example, the amount owed after adding that interest is CAD 210.
These examples use simple, stated information for one year. They do not describe how every real account or loan works. Real terms can include other details, so read the information provided before making a comparison.
interest=starting amount×stated rate\text{interest} = \text{starting amount} \times \text{stated rate}
  • Find the starting amount and the rate.
  • Check the time period attached to the rate.
  • For these examples, calculate the stated percent of the starting amount.

Include fees in the comparison

A fee can make an account cost money even when it pays interest. To compare the two amounts, first identify the fee and the period it covers. Then compare the total fees with the interest earned over that same stated period.
For instance, a hypothetical account might pay CAD 8 in interest over a stated period and charge CAD 3 per month for four months. The fees for four months total CAD 12. In that example, the fees are CAD 4 more than the interest. This comparison does not include any other changes to the account.
Loans can also have fees. If a loan has interest and a fee, both can affect the total cost of borrowing. Do not treat the interest rate as the only cost. Read whether the fee is charged once, each month, or at another stated time.
When the information gives different time periods, do not compare the amounts until you know what period each one covers. Use only the details that are stated. If a detail is missing, say that you cannot make a complete comparison from the information provided.
total fees\text{total fees} = fee per period × number of periods
  • Add repeated fees for the stated number of periods.
  • Compare interest and fees over matching periods.
  • A low interest rate does not by itself show the full cost.

A careful way to explain your thinking

When explaining an account or loan, name the starting amount, the interest rate, and the time period. Then say whether interest is paid or charged. State any fees separately. This makes it easier for another person to follow your comparison.
For practice, imagine two hypothetical accounts. One pays a stated amount of interest but also charges a monthly fee. The other has no fee but pays less interest. You cannot decide which is better by looking at just one number. You need the interest and fees for the same period, along with any other details the question provides.
Do not assume that a fee is charged every month unless the information says so. Do not assume that interest is added for a longer period than the one stated. Good explanations separate facts from guesses.
  • Use the stated information rather than guessing.
  • Explain the effect of interest and fees separately.
  • Compare amounts for the same time period.

Worked example

Interest paid into an account

Hypothetical example: An account has CAD 150. It pays 4% interest for one year. There are no fees in this example. How much interest is paid, and what is the amount after the interest is added?
Starting amount and interest
Starting amount and interestHypothetical one-year account example. The two bars show the starting amount and interest paid.150 CADStarting amount (CAD)6 CADInterest (CAD)

Hypothetical one-year account example. The two bars show the starting amount and interest paid.

  1. Find the interest
    The rate applies to CAD 150 for one year. Find 4% of CAD 150. Since 4% is four hundredths, the interest is CAD 6.
    150×0.04=6150 \times 0.04 = 6
  2. Add the interest
    The account began with CAD 150. Add the CAD 6 paid as interest to find the amount after interest is added.
    150+6=156150 + 6 = 156
Answer: The account earns CAD 6 in interest. The amount after the interest is added is CAD 156.
Check: The interest is less than the starting amount, which makes sense for a rate of 4%.

Worked example

Interest charged on a loan

Hypothetical example: A person borrows CAD 240. The loan charges 5% interest for one year. No fees or payments are included. Find the interest for the year and the amount after it is added.
Loan amount and interest
Loan amount and interestHypothetical one-year loan example. The bars show the amount borrowed and the interest charged.240 CADAmount borrowed (CAD)12 CADInterest (CAD)

Hypothetical one-year loan example. The bars show the amount borrowed and the interest charged.

  1. Find the interest charged
    The loan charges 5% of CAD 240 for the stated year. Find one twentieth of CAD 240, which is CAD 12.
    240×0.05=12240 \times 0.05 = 12
  2. Add the interest to the borrowed amount
    In this example, no payments or fees change the amount. Add the CAD 12 interest to the CAD 240 borrowed to find the amount after interest is added.
    240+12=252240 + 12 = 252
Answer: The interest for the year is CAD 12. The amount after it is added is CAD 252.
Check: Because the loan charges interest, the amount owed in this example is greater than the amount borrowed.

Worked example

Compare interest with account fees

Hypothetical example: An account earns CAD 10 in interest over four months. It also charges a fee of CAD 2 each month. Find the total fees and explain how they compare with the interest.
Interest and fees over four months
Interest and fees over four monthsHypothetical example. The bars compare interest earned and total fees for the same four-month period.10 CADInterest (CAD)8 CADTotal fees (CAD)

Hypothetical example. The bars compare interest earned and total fees for the same four-month period.

  1. Find the total fees
    The fee is CAD 2 for each of four months. Add four groups of CAD 2 to find the total fees.
    2×4=82 \times 4 = 8
  2. Compare the amounts
    The account earns CAD 10 in interest and charges CAD 8 in fees over the same four months. The interest is CAD 2 more than the fees. This compares only the two stated amounts.
    10−8=210 - 8 = 2
Answer: The total fees are CAD 8. The stated interest is CAD 2 more than the fees.
Check: Both amounts cover four months, so they can be compared directly. This does not establish the full result if other charges or changes exist.

Common mistakes and how to avoid them

Thinking an interest rate and a fee are the same thing.
Correction: Interest is based on an amount and a stated rate. A fee is a separate charge. Identify each one on its own.
Looking only at the rate when comparing accounts or loans.
Correction: Include any stated fees. They can change how much an account earns or how much a loan costs.
Comparing interest for one time period with fees for another.
Correction: Check that both amounts cover the same period before comparing them.
Assuming a fee repeats or that interest applies for more time than stated.
Correction: Use only the timing given in the information. If timing is missing, say that you need more information.

Lesson summary

  • An interest rate tells what part of an amount is paid or charged for a stated time.
  • Interest can be added to money in an account or to money owed on a loan.
  • Fees are separate charges and can change the cost or benefit.
  • A fair comparison uses the stated amounts over the same time period.

Check your understanding

Question 1

A hypothetical account has CAD 300 and pays 2% interest for one year. There are no fees. How much interest is paid?
  1. CAD 6
  2. CAD 2
  3. CAD 30
  4. CAD 302
Show answer and explanation
CAD 6
2% of CAD 300 is CAD 6. The other choices do not give the interest amount.

Question 2

A hypothetical loan charges CAD 4 in fees each month for three months. What are the total fees for those months?
  1. CAD 7
  2. CAD 12
  3. CAD 4
  4. CAD 3
Show answer and explanation
CAD 12
There are three fees of CAD 4, so the total is CAD 12.

Question 3

Why should you check the time period before comparing interest and fees?
  1. So both amounts cover the same period.
  2. So you can ignore the fees.
  3. So the interest rate becomes a fee.
  4. So you can assume missing details.
Show answer and explanation
So both amounts cover the same period.
Amounts for matching periods can be compared fairly. Missing details should not be guessed.

Key terms

Starting amount
The amount first saved in an account or borrowed as a loan.
Interest
Money paid on savings or charged for borrowing.
Interest rate
The stated part of an amount used to work out interest for a stated time.
Annual
For one year.
Fee
A charge for a service or for using an account or loan.
Hypothetical
Made up for learning, rather than presented as a real offer.

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Published by DoAssignment. This reviewed lesson follows Ontario Grade 6 Mathematics, expectation F1.4. It is a study resource, not an official curriculum publication.

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