B3.5 Compare payment frequencies and total interest

Ontario Grade 11 Mathematics

Saving, Investing, and Borrowing

MEL3E study topic B3.5: Use loan information and repeated calculations to compare payment options.

A loan offer might let you pay monthly, every two weeks, or weekly. The schedule changes how often money leaves your account. It can also change how much interest you pay overall. To compare options fairly, first check that they are for the same amount borrowed and the same loan term. Then use the payment details and, when needed, a calculator or spreadsheet to compare total payments and total interest. This lesson uses repeated balance calculations or lender-style quote results, not a shortcut formula.

What you will learn

Explain what a payment frequency is.
Compare payment options for the same loan using reliable quote or spreadsheet results.
Calculate total paid and total interest from payment information.
Choose a payment schedule by considering both cost and how often payments are due.

Start with a fair comparison

A payment frequency is how often you make a loan payment. Monthly means once each month. Biweekly means once every two weeks. Weekly means once each week. A loan term is the length of time allowed to repay the loan.

Before comparing payment schedules, check that the amount borrowed, interest rate, and term are the same. Also check whether the lender is offering regular biweekly payments or accelerated biweekly payments. They are not always the same: an accelerated plan may use a larger payment and can pay the loan off sooner.

A smaller payment does not always mean a cheaper loan. It may simply be due more often or continue for longer. Compare the total amount paid over the full loan, not just one payment.

Keep the loan amount, rate, and term consistent when comparing.
Confirm how many payments are due and whether the schedule is accelerated.
Compare total cost as well as payment size.

Find total paid and total interest

The total paid is the payment amount multiplied by the number of payments. Total interest is the amount paid above the amount borrowed. For example, if someone borrows CAD 4,000 and repays CAD 4,360 altogether, the total interest is CAD 360.

A lender's quote or a spreadsheet may show the payment amount and the number of payments. Multiply those two values to get total paid. Then subtract the original loan amount to find total interest. Keep money amounts to the nearest cent when the quote gives cents.

A spreadsheet can also repeat the balance calculation for each payment. Start with the amount still owed. Add that period's interest, then subtract the payment. The new balance becomes the starting balance for the next row. This matters because interest is calculated on the balance still owed, not on the original amount every time.

\text{Total interest}=\text{total paid}-\text{amount borrowed}

Total paid = payment amount × number of payments.
Total interest = total paid − amount borrowed.
Repeated balance calculations use the previous row's ending balance.

Use a calculator or spreadsheet carefully

When a lender provides payment estimates for different frequencies, record the payment amount, payment count, total paid, and total interest for each option. Check that the quote uses the same loan amount and term. If the quote does not show total interest, calculate it from the totals.

For a repeated spreadsheet calculation, use one row for each payment. A row can show the starting balance, interest for that period, payment, and ending balance. The ending balance should be carried into the next row. Use the rate per payment period specified by the lender or by the comparison tool. Do not assume that a stated annual rate can be used unchanged for every payment period.

Small differences can happen because of rounding or lender fees. Use the same rounding approach for both options, and include fees only if the quote includes them. A spreadsheet result is only as useful as its inputs.

Use the lender's stated rate for each payment period.
Check inputs and payment counts before trusting a result.
A lower total interest is a cost advantage, but payment timing must also fit the borrower's budget.

Make a decision using more than one number

A useful comparison answers two questions: Which option costs less overall, and can the borrower manage each payment when it is due? Weekly payments may be smaller than monthly payments, but there are more of them. A borrower who is paid weekly may find that schedule easier to plan for.

Do not choose only by looking at the smallest payment. A lower payment can be linked to a longer term and more total interest. Read the full quote and compare both the schedule and the total cost.

Compare total interest and payment amount together.
Consider whether payment dates match the borrower's income and budget.
State the reason for the choice using the figures.

What to record when comparing quotes

Item	Monthly option	Other frequency
Amount borrowed	Same loan amount	Same loan amount
Payment amount	Record quote	Record quote
Number of payments	Count for full term	Count for full term
Total paid	Payment × count	Payment × count
Total interest	Total paid − amount borrowed	Total paid − amount borrowed

Worked example

Compare two quotes for a used car loan

A dealership gives two quotes for the same CAD 8,000 loan over two years at the same stated rate. The monthly quote is CAD 361.05 for 24 payments. The biweekly quote is CAD 166.64 for 52 payments. Treat these as quote figures from the lender's calculator. Which schedule has less total interest?

Check the comparison
Both quotes are for the same amount and term, so the totals can be compared. The lender's calculator has already accounted for its rate and payment schedule.
Find the monthly total
Multiply the monthly payment by the 24 payments. This gives the total amount paid over the quoted term.
$361.05\times24=\text{CAD }8,665.20$
Find monthly interest
Subtract the borrowed amount from the total paid. The amount left is the total interest in this quote.
$8,665.20-8,000=\text{CAD }665.20$
Find the biweekly total and interest
Repeat the same steps for the biweekly quote. Using the same subtraction makes the comparison fair.
$166.64\times52=\text{CAD }8,665.28; 8,665.28-8,000=\text{CAD }665.28$

Answer: The monthly quote has CAD 0.08 less total interest. The difference is very small, and the biweekly payment is due more often. The borrower should check the lender's final figures and choose a schedule that fits the budget.

Check: The monthly total is CAD 8,665.20 and the biweekly total is CAD 8,665.28. Both totals are above CAD 8,000, so both have positive total interest.

Worked example

Compare spreadsheet totals for equipment financing

A worker compares two lender estimates for the same CAD 5,000 equipment loan and the same term. The spreadsheet repeats the balance calculation using the lender's period rates and rounds each displayed payment to cents. The monthly option shows 36 payments of CAD 156.67. The weekly option shows 156 payments of CAD 36.20. Find total paid and total interest for each, then identify the lower-cost option based on these displayed figures.

Calculate the monthly total
Multiply the displayed payment by the number of monthly payments. This uses the full payment count, not just a typical month.
$156.67\times36=\text{CAD }5,640.12$
Calculate monthly interest
Subtract the original amount borrowed from the monthly total to find how much is paid above the loan amount.
$5,640.12-5,000=\text{CAD }640.12$
Calculate the weekly total
Multiply the weekly payment by all 156 payments. Weekly payments continue throughout the full quoted term.
$36.20\times156=\text{CAD }5,647.20$
Calculate weekly interest and compare
Subtract the same original loan amount. Compare the two interest totals, while remembering that displayed payments rounded to cents can cause a small difference from the lender's exact spreadsheet total.
$5,647.20-5,000=\text{CAD }647.20$

Answer: The weekly option has CAD 647.20 in interest, compared with CAD 640.12 for the monthly option. Based on the displayed figures, the monthly option costs CAD 7.08 less in total interest. The weekly payment is smaller each time, but it is due much more often.

Check: The weekly total is CAD 5,647.20, which is CAD 7.08 more than the monthly total of CAD 5,640.12. The interest totals differ by the same CAD 7.08 because both options borrow CAD 5,000.

Common mistakes and how to avoid them

Choosing the option with the smallest single payment.

Correction: Multiply by the full number of payments and compare total interest as well.

Comparing quotes with different loan amounts or terms.

Correction: Confirm that the main loan details match before deciding which frequency costs less.

Using the annual rate as the rate for every payment period.

Correction: Use the period rate stated by the lender or its calculator. Do not change or guess the rate.

Subtracting the total paid from the amount borrowed.

Correction: Subtract the amount borrowed from total paid. Interest is the amount paid above the loan amount.

Lesson summary

Payment frequency tells how often payments are due.
Compare schedules for the same loan amount and term.
Find total paid by multiplying payment amount by payment count.
Find total interest by subtracting the amount borrowed from total paid.
Use quote or spreadsheet results carefully, and consider both cost and payment timing.

Check your understanding

Question 1

A quote is for CAD 3,000. It requires 40 payments of CAD 81.50. What is the total interest based on these figures?

CAD 260
CAD 3,260
CAD 3,815
CAD 260.00

Show answer and explanation

CAD 260

Total paid is CAD 81.50 × 40 = CAD 3,260. Subtract CAD 3,000 borrowed, giving CAD 260 in total interest.

Question 2

Two quotes have the same loan amount and term. One has smaller payments, but many more of them. What should you compare before deciding?

Only the smallest payment
The total paid and total interest, as well as payment timing
Only the number of payments
The borrower's age

Show answer and explanation

The total paid and total interest, as well as payment timing

A small payment alone does not show the total cost. Compare the full payment totals and whether the schedule fits the budget.

Key terms

Payment frequency: How often a loan payment is due, such as monthly, biweekly, or weekly.
Loan term: The length of time allowed for repaying a loan.
Total paid: The sum of all payments made over the quoted loan term.
Total interest: The part of the total paid that is above the amount borrowed.
Balance: The amount still owed at a point in the repayment schedule.

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About this lesson

Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Mathematics (MEL3E), expectation B3.5. It is a study resource, not an official curriculum publication.

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B3.5 · Compare payment frequencies and total interest