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F1.6 · Compare account and loan rates and fees for different scenarios

Learn to compare account and loan rates and fees for different scenarios through clear examples and targeted practice.

Ontario Grade 7 Mathematics

Financial Literacy

Use the stated numbers to compare what you earn or pay

An account or loan may include a rate and fees. An account rate can tell how much interest you earn. A loan rate can tell how much interest you pay. A fee is a separate cost. So, the option with the highest account rate or lowest loan rate is not always the better choice. To compare fairly, use the same amount and time period when the scenario allows it. All amounts and rates in this lesson are hypothetical examples, not current offers.

What you will learn

  • Identify an amount, rate, fee, and time period in a scenario.
  • Compare account gains after fees.
  • Compare loan costs, including fees.
  • Explain which choice fits a stated situation and why.

Read each scenario carefully

Before calculating, find four details: the amount, rate, fee, and time period. The amount is the money in the account or borrowed. A rate describes interest in relation to an amount. Interest is money earned in an account or charged on a loan. A fee is a separate amount paid for an account or service.
A rate may be written as a percent per year. The words “per year” tell you the time period. For a fair comparison, match the time period and amount when possible. If the periods differ and the scenario gives no way to make them match, explain that you cannot fairly compare the options from the information given.
A percent means a number of parts out of 100. For example, 1% means 1 out of every 100. In these examples, the scenario says to use simple interest. That means interest is calculated on the starting amount only. Do not assume this method if a scenario does not state how to calculate interest.
When a rate is given as a percent, write it as a number of hundredths to calculate the stated interest. For example, 2% is 0.02. Multiply that number by the amount to find one-year simple interest.
interest=rate as a decimal×amount\text{interest} = \text{rate as a decimal} \times \text{amount}
  • Record the amount, rate, fee, and time period.
  • Check how often a fee applies.
  • Use only the interest method stated in the scenario.

Compare account choices

Interest adds money to an account. Fees take money away. To compare an account's gain after fees, find the interest for the stated period and subtract the fees for that same period.
For example, an account that earns CAD 12 interest and charges a CAD 5 fee has a gain of CAD 7 after that fee. Another account that earns CAD 9 and charges no fee has a gain of CAD 9. The second account gives the greater gain in this example, even though its interest is lower.
Read fee wording closely. A fee charged “each month” is counted once for each month in the comparison period. A fee charged “once” is counted one time. If the timing is unclear, do not guess; say what detail is missing.
account gain after fees=interest earned−fees\text{account gain after fees} = \text{interest earned} - \text{fees}
  • Subtract account fees from interest earned.
  • Compare the gains for the same period.
  • A higher account rate does not guarantee a greater gain after fees.

Compare loan choices

For a loan, interest and fees are costs. Find the interest charged for the stated period, then add the fees that apply. Compare the total costs for the same loan amount and time period when possible.
A lower loan rate does not always mean a lower total cost. A larger fee may make that loan more expensive. State the costs and the period when you explain your choice.
Keep account and loan calculations separate. Subtract fees from account interest to find an account gain. Add fees to loan interest to find a loan cost.
loan cost=interest charged+fees\text{loan cost} = \text{interest charged} + \text{fees}
  • Add loan fees to interest charged.
  • The smaller total cost is less expensive for that scenario.
  • Do not compare different amounts or periods as if they were the same.

Use a clear comparison routine

First, mark the amount and time period. Next, list each rate and fee. Calculate the interest using the stated method. Count fees according to their wording. Then find each account gain or loan cost and compare the results.
A labelled chart can help show final amounts. Label what each bar represents, such as “gain after fees” or “loan cost.” A chart of rates alone may not answer the question when fees also matter.
Practice with this routine: for an account, ask, “What is the interest after fees?” For a loan, ask, “What is the cost after adding fees?” Explain your choice using the calculated amounts, not only the rates.
  • Use the same amount and period for a fair comparison.
  • Combine interest and fees in the correct way for the situation.
  • If information is missing, name what is needed instead of making it up.

What to combine

SituationCalculationMeaning
AccountInterest earned minus feesGain after fees
LoanInterest charged plus feesTotal cost

Worked example

Compare two hypothetical accounts

Mina compares two hypothetical accounts for one year. Each starts with CAD 500. Account A earns 2% simple interest per year and charges a CAD 4 fee for the year. Account B earns 1.5% simple interest per year and has no fee. Which gives the greater gain after fees?
One-year account gains after fees
One-year account gains after feesHypothetical data. Each bar shows the gain after fees, in CAD.6 CADAccount A7.5 CADAccount B

Hypothetical data. Each bar shows the gain after fees, in CAD.

  1. Find Account A's interest
    Write 2% as 0.02. Multiply by CAD 500 to find the one-year interest.
    0.02×500=100.02 \times 500 = 10
  2. Subtract Account A's fee
    The fee reduces the account gain, so subtract CAD 4 from the interest.
    10−4=610 - 4 = 6
  3. Find Account B's interest
    Account B has no fee, so its interest is also its gain after fees.
    0.015×500=7.500.015 \times 500 = 7.50
Answer: Account B gives the greater gain after fees: CAD 7.50, compared with CAD 6 for Account A.
Check: The starting amounts and time periods match. Account A's fee is subtracted, while Account B has no fee.

Worked example

Compare two hypothetical loans

Ari compares two hypothetical loans of CAD 800 for one year. Loan X charges 3% simple interest per year and a CAD 10 fee. Loan Y charges 2.5% simple interest per year and a CAD 18 fee. Which has the lower cost for the year?
One-year loan costs
One-year loan costsHypothetical data. Each bar shows interest plus fees, in CAD.34 CADLoan X38 CADLoan Y

Hypothetical data. Each bar shows interest plus fees, in CAD.

  1. Calculate Loan X interest
    Write 3% as 0.03 and multiply by CAD 800.
    0.03×800=240.03 \times 800 = 24
  2. Add Loan X's fee
    A loan fee adds to the interest cost.
    24+10=3424 + 10 = 34
  3. Calculate Loan Y's total cost
    Find 2.5% of CAD 800, then add the CAD 18 fee.
    0.025×800+18=380.025 \times 800 + 18 = 38
Answer: Loan X has the lower cost for the year: CAD 34 compared with CAD 38 for Loan Y.
Check: Loan Y has the lower rate, but its larger fee makes its total cost higher in this scenario.

Worked example

Count fees charged each month

Two hypothetical accounts each hold CAD 600 for three months. Account P earns CAD 3 interest over those three months and charges a CAD 2 fee each month. Account Q earns CAD 4 interest over the same period and charges one CAD 1 fee for the period. Which gives the greater gain after fees?
Fees over three months
Fees over three monthsHypothetical data. The bars compare total fees, in CAD; they do not show account gains.6 CADAccount P1 CADAccount Q

Hypothetical data. The bars compare total fees, in CAD; they do not show account gains.

  1. Count Account P's fees
    The CAD 2 fee is charged each month. Count one fee for each of the three months.
    3×2=63 \times 2 = 6
  2. Find Account P's gain after fees
    Subtract its total fees from its stated interest. The negative result means the fees are greater than the interest.
    3−6=−33 - 6 = -3
  3. Find Account Q's gain after fees
    Account Q has one CAD 1 fee for the whole period.
    4−1=34 - 1 = 3
Answer: Account Q gives the greater gain after fees: CAD 3. Account P is down CAD 3 after fees.
Check: Both accounts use the same three-month period. Account P's fee is counted three times because it is charged each month.

Common mistakes and how to avoid them

Choosing an account only because it has the higher rate.
Correction: Calculate interest and subtract the fees for the same period. Compare the gains after fees.
Choosing a loan only because it has the lower rate.
Correction: Add fees to interest charged. Compare the total costs for the same amount and period.
Counting a monthly fee only once over several months.
Correction: Read how often the fee applies. Count it once for each stated month.
Comparing different time periods as if they match.
Correction: Use matching periods, or explain that the information is not enough for a fair comparison.

Lesson summary

  • Rates, fees, amounts, and time periods all matter.
  • For an account, subtract fees from interest earned to find the gain after fees.
  • For a loan, add fees to interest charged to find the cost.
  • Use the stated details and explain your comparison.

Check your understanding

Question 1

A hypothetical account earns CAD 8 interest in one year and charges a CAD 3 fee for that year. What is its gain after fees?
  1. CAD 5
  2. CAD 11
  3. CAD 8
  4. CAD 3
Show answer and explanation
CAD 5
Subtract the fee from the interest: CAD 8 minus CAD 3 is CAD 5.

Question 2

Two hypothetical loans have the same amount and period. Loan A has CAD 20 interest and a CAD 7 fee. Loan B has CAD 18 interest and a CAD 12 fee. Which costs less?
  1. Loan A, at CAD 27
  2. Loan B, at CAD 30
  3. Loan B, at CAD 18
  4. They cost the same
Show answer and explanation
Loan A, at CAD 27
Loan A costs CAD 27 in total. Loan B costs CAD 30. Loan A costs less.

Question 3

A hypothetical account charges a CAD 2 fee each month for four months. What is the total fee for the four-month period?
  1. CAD 8
  2. CAD 6
  3. CAD 2
  4. CAD 4
Show answer and explanation
CAD 8
There are four fees of CAD 2, so the total fee is CAD 8.

Key terms

Rate
A percent that describes interest earned or charged for a stated period.
Interest
Money earned in an account or charged on borrowed money.
Fee
An amount paid for an account or service, separate from interest.
Loan
Money borrowed that must be repaid under the stated terms.
Gain after fees
Interest earned after subtracting the fees paid.

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Published by DoAssignment. This reviewed lesson follows Ontario Grade 7 Mathematics, expectation F1.6. It is a study resource, not an official curriculum publication.

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