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B2.1 · Compare savings alternatives, services, and fees

Learn to compare savings alternatives, services, and fees through clear examples and targeted practice.

Ontario Grade 11 Mathematics

Personal Finance

Comparing savings alternatives, services, and fees | MBF3C study topic B2.1

Saving means setting money aside for later. A savings alternative is an account or other option for holding savings. Alternatives can differ in their interest rates, fees, services, and rules for using the money. A higher rate does not always mean a better choice. A fee can reduce or erase the extra interest, and a service is useful only if it fits the saver’s needs. In this lesson, all money amounts are in Canadian dollars (CAD).

What you will learn

Compare savings alternatives using rates, fees, services, and access rules.
Estimate interest after applicable fees for a stated period.
Recommend an option using the saver’s needs and the comparison evidence.

1. Start with the saver’s needs

Before comparing alternatives, find out what the saver plans to do. They may want to reach their money easily, avoid fees, or earn interest while saving toward a goal. Different savers can reasonably choose different options because their needs are not always the same.

Interest is money earned for keeping savings in an account. An interest rate tells how much interest is earned over a stated period. An annual rate is a rate for one year. Check the period before comparing rates; rates for different periods are not a fair comparison until they are put on the same time basis.

A fee is a charge for an account or service. It might be charged each month, each year, or only when a certain activity happens. For example, an account may charge for a withdrawal or transfer. Include a fee only when it applies to the saver’s situation.

Services and access rules are part of the offer too. One alternative might make it easier to access cash or transfer money. Another might offer a service the saver does not need. A minimum balance is the least amount that must stay in an account under its rules. Check whether the saver can meet that condition and whether it affects fees or access.

Ask what the saver needs before choosing.
Compare rates that cover the same period.
Check when each fee applies.
Consider services, access, and minimum-balance rules.

2. Make a fair numerical comparison

To compare two alternatives, use the same starting amount and the same length of time. This lets you see how each offer works for the same saving plan. If the plans involve different withdrawals, account for the fees that each plan would trigger.

A simple estimate of interest can be made when the problem gives an annual rate and asks about a stated time. Simple interest is an estimate based on the starting amount, the annual rate, and the time saved. The starting amount is the money put into savings at the beginning. Convert a percentage to a decimal before multiplying: for example, 2% is

0.02

. Express time in years, so six months is

0.5

years.

The letters in the estimate formula stand for the quantities in the comparison:

I

is estimated interest,

P

is the starting amount,

r

is the annual rate written as a decimal, and

t

is the time in years. Once you have estimated the interest, subtract applicable fees for the same period. The result is an estimate of interest after fees. It is not necessarily the account’s complete ending balance.

For a monthly fee, count the months in the comparison period and add the charges that apply. For a withdrawal fee, include it only if the saver expects to make the withdrawal that triggers it. Do not subtract a fee that does not apply to the stated plan.

I=Prt

Hold the starting amount and time period constant.
Change a percentage rate to a decimal for the estimate.
Add up fees over the same time period.
Include fees that match the saver’s plan, not fees that do not apply.

3. Compare the full offer

Consider this one-year comparison for CAD 1,000 with no withdrawals. Option A earns an estimated CAD 20 before fees and has no annual fee. Option B earns CAD 30 before fees, but its CAD 18 annual fee leaves CAD 12 after fees. Option B has the higher rate, but Option A leaves more estimated interest after its fee is considered.

The numbers are only part of the decision. A saver who needs frequent withdrawals may prefer an alternative with easy access and low withdrawal costs. A saver who expects to leave the money untouched may put more weight on the estimated interest after fees. Neither preference is automatically right for everyone; the details of the saver’s plan matter.

Check the conditions attached to a service or fee. A fee might be waived when a balance meets a stated amount, for example. Do not assume the saver qualifies for a waiver unless the comparison says so. If information is missing or unclear, say what you would need to check rather than guessing.

A useful comparison explains both the advantages and the trade-offs. One option could leave more estimated interest but charge for withdrawals. Another could have a lower estimate but provide access or services that fit the saver better.

A higher interest rate can still leave less after fees.
Compare fees and interest for the same period.
Match access and services to the saver’s likely use.
State important conditions and trade-offs.

4. Recommend with evidence

A clear recommendation links the saver’s needs to the comparison. First, identify what matters most to the saver. Next, compare the estimated interest after applicable fees. Then, consider services, access, and any conditions that could affect the choice. Use these points to explain why one alternative better fits the stated plan.

For example, if both alternatives meet the saver’s access needs and one leaves more estimated interest after fees, that may support recommending it. If the saver expects frequent withdrawals, a withdrawal charge could change the decision. Mention that condition so the recommendation is not based on the rate alone.

Keep the limits of the estimate clear. It uses the stated starting amount, rate, time, and fees. It does not account for details that the comparison does not provide. A recommendation is strongest when it explains what information it used and why that information matters.

Use the saver’s needs and the figures as evidence.
Explain why a service or fee matters to the plan.
Name conditions that could change your recommendation.

One-year comparison for CAD 1,000 with no withdrawals

Option	Annual rate	Annual fee	Interest before fee	Interest after fee
A	2%	CAD 0	CAD 20	CAD 20
B	3%	CAD 18	CAD 30	CAD 12

Worked example

Example 1: Compare annual fees

Mina plans to leave CAD 2,000 in an account for one year and make no withdrawals. Option A pays 2.4% per year and has no annual fee. Option B pays 3% per year and charges CAD 18 per year. Both meet Mina’s access needs. Which option gives more estimated interest after fees?

Estimate Option A
Use the starting amount and one-year period. Write 2.4% as the decimal 0.024 and estimate the interest. Because Option A has no annual fee, there is nothing to subtract.
$2{,}000\times0.024\times1=48$
Estimate Option B after its fee
Write 3% as 0.03 and estimate one year of interest. The annual fee applies during Mina’s one-year plan, so subtract CAD 18.
$2{,}000\times0.03\times1-18=42$
Compare the estimates
Option A leaves an estimated CAD 48 after fees, while Option B leaves CAD 42. Since both options meet Mina’s access needs, Option A is the better fit based on these figures.

Answer: Option A gives CAD 6 more estimated interest after fees over one year.

Check: Option B earns CAD 60 before its fee; subtracting CAD 18 leaves CAD 42. Option A earns CAD 48 with no fee. The difference is CAD 6.

Worked example

Example 2: Account for a planned withdrawal

Jordan expects to save CAD 1,500 for six months and make one withdrawal. Option C pays 2% per year, has no monthly fee, and charges CAD 4 for that withdrawal. Option D pays 1.5% per year, charges CAD 1 per month, and has no withdrawal fee. Both provide the access Jordan needs. Which has more estimated interest after fees?

Estimate Option C
Six months is half a year. Write 2% as 0.02 and estimate the interest for half a year. Jordan plans one withdrawal, so subtract the CAD 4 withdrawal fee.
$1{,}500\times0.02\times0.5-4=11$
Estimate Option D
Write 1.5% as 0.015 and estimate the interest for half a year. Six monthly fees apply, so subtract CAD 6 in total.
$1{,}500\times0.015\times0.5-(6\times1)=5.25$
Compare the estimates
Option C leaves an estimated CAD 11 after fees, compared with CAD 5.25 for Option D. Given Jordan’s stated plan and access needs, Option C gives the greater estimate.

Answer: Option C gives CAD 5.75 more estimated interest after fees over six months.

Check: Option C earns CAD 15 before its withdrawal fee, leaving CAD 11. Option D earns CAD 11.25 before monthly fees, leaving CAD 5.25. The difference is CAD 5.75.

Common mistakes and how to avoid them

Choosing the highest rate without checking fees.

Correction: Estimate the interest for the same period, then subtract the fees that apply.

Subtracting a fee that the saver’s plan would not trigger.

Correction: Check the conditions and include only fees that apply to the stated plan.

Comparing a monthly fee with a year of interest without adding all monthly charges.

Correction: Count the months in the comparison period and total the applicable monthly fees.

Saying one option is best for everyone.

Correction: Connect your recommendation to the saver’s needs, access, services, and plan.

Lesson summary

Identify the saver’s priorities, including access and useful services.
Compare alternatives using the same starting amount and time period.
Estimate interest and subtract the fees that apply.
Support a recommendation with both the figures and the saver’s needs.

Check your understanding

Question 1

Rae saves CAD 800 for one year with no withdrawals. Option P pays 2% per year and has no fee. Option Q pays 2.5% per year and charges CAD 5 per year. Which has greater estimated interest after fees?

Option P by CAD 1
Option Q by CAD 1
They are equal
Option Q by CAD 4

Show answer and explanation

Option P by CAD 1

Option P earns CAD 16 with no fee. Option Q earns CAD 20 before its fee and CAD 15 after the fee. Option P is greater by CAD 1.

Question 2

An account charges CAD 2 each month. If the charge applies every month, what are the fees over six months?

CAD 2
CAD 8
CAD 12
CAD 24

Show answer and explanation

CAD 12

There are six monthly charges of CAD 2, for a total of CAD 12.

Question 3

A saver expects to withdraw money often. What should you check when comparing options?

Only the advertised annual rate
Withdrawal fees and access services, as well as the rate
Only the account name
A rate from a different comparison period

Show answer and explanation

Withdrawal fees and access services, as well as the rate

Frequent withdrawals make access and withdrawal fees important, along with the rate.

Key terms

Annual rate: An interest rate stated for one year.
Fee: A charge for an account or service.
Minimum balance: The least amount required to remain in an account under its rules.
Simple interest: An estimate of interest based on the starting amount, annual rate, and time saved.
Withdrawal: Taking money out of an account.

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About this lesson

Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Mathematics (MBF3C), expectation B2.1. It is a study resource, not an official curriculum publication.

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