B3.4 · Investigate how repayment time affects principal and interest

Ontario Grade 11 Mathematics

Saving, Investing, and Borrowing

A Grade 11 MEL3E lesson on comparing loan repayment plans

What you will learn

• Explain how repayment time affects the amount of interest paid.
• Use repeated calculations or a spreadsheet to track a loan balance.
• Compare repayment plans while keeping the starting loan and interest rate the same.
• Use both total interest and payment size when making a repayment decision.

1. Follow where each payment goes

• Interest is charged while money is still owed.
• Subtract the interest portion from the payment to find how much principal is repaid.
• A lower balance usually means less interest in the next period when the rate is unchanged.

2. Use repeated calculations or a spreadsheet

• Repeat the same calculation for each period.
• Use the ending balance of one period as the starting balance of the next.
• Compare plans with the same loan amount and interest rate to focus on repayment time.

3. Decide what the comparison shows

• More repayment periods can mean more total interest.
• A smaller regular payment is not automatically the lower-cost choice.
• Balance affordability against the total cost shown by the repayment schedule.

Example 2 repayment comparison

Worked example

Example 1: Compare two plans for a work laptop

1. Calculate the first month's interest
   Interest for the first month is 1% of CAD 1,200. One percent is the same as 0.01, so the first month's interest is CAD 12.
   $$1{,}200 \times 0.01 = 12$$
2. Track the CAD 220 plan
   In month 1, CAD 12 of the payment covers interest, leaving CAD 208 to reduce the balance to CAD 992. Repeat the calculation using each new balance. The first five payments are CAD 220; after the fifth, the balance is about CAD 138.99. In month 6, interest is about CAD 1.39, so the final payment is about CAD 140.38.
   $$1{,}200 \rightarrow 992 \rightarrow 781.92 \rightarrow 569.74 \rightarrow 355.44 \rightarrow 138.99 \rightarrow 0$$
3. Find the total for the faster plan
   There are five regular payments of CAD 220 and one final payment of about CAD 140.38. Add them to find the total paid, then subtract the original CAD 1,200 to find total interest.
   $$5(220) + 140.38 = 1{,}240.38$$
4. Track and total the CAD 130 plan
   Repeat the same monthly steps with a CAD 130 payment. After nine regular payments, the balance is about CAD 94.51. The tenth month's interest is about CAD 0.95, making the final payment about CAD 95.46. The plan takes longer and has more total interest.
   $$9(130) + 95.46 = 1{,}265.46$$

Worked example

Example 2: Choose between two plans for a repair

1. Calculate the first period for each plan
   Both plans start with the same CAD 1,000 balance, so the first month's interest is CAD 10. With a CAD 510 payment, CAD 500 reduces principal, leaving CAD 500. With a CAD 260 payment, CAD 250 reduces principal, leaving CAD 750.
   $$1{,}000 + 10 - 510 = 500$$
2. Finish the CAD 510 plan
   In month 2, interest on CAD 500 is CAD 5. The remaining amount owed is CAD 505, so the final payment is CAD 505. The total paid is CAD 1,015, which is CAD 15 more than the original principal.
   $$1{,}000 + 15 = 1{,}015$$
3. Finish the CAD 260 plan
   Continue using the new balance each month. After three CAD 260 payments, the balance is about CAD 242.48. Month 4 interest is about CAD 2.42, so the final payment is about CAD 244.90. This plan takes 4 months, and its total is about CAD 1,024.90.
   $$3(260) + 244.90 = 1{,}024.90$$
4. Compare time and cost
   The CAD 510 plan takes 2 months and has CAD 15 in interest. The CAD 260 plan takes 4 months and has about CAD 24.90 in interest. The faster plan costs less interest, but its regular payment is much larger. A suitable choice must also fit the borrower's budget.
   $$1{,}024.90 - 1{,}000 = 24.90$$

Common mistakes and how to avoid them

Lesson summary

• Each period, interest is added to the balance and the payment is subtracted.
• The part of the payment left after interest reduces principal.
• Compare repayment time by tracking the balance repeatedly or using a spreadsheet.
• A longer plan often lowers regular payments but can increase total interest.
• Use total interest and payment affordability together when comparing plans.

Check your understanding

Key terms

Balance

The amount still owed on a loan.

Interest

The cost of borrowing money, calculated under the loan's terms.

Principal

The amount borrowed, not including interest.

Repayment schedule

A list showing payments, interest, and the balance over time.

Total paid

The sum of all payments made to repay the loan.

Continue through MEL3E

View the complete Ontario Grade 11 Mathematics learning path

• B1.1 · Compare savings services, costs, and ways to reduce fees
• B1.2 · Compare credit-card and debit-card costs and incentives
• B1.3 · Read financial statements and use them to manage money
• B2.1 · Investigate and solve simple-interest problems
• B2.2 · Calculate compound interest by repeated simple-interest steps
• B2.3 · Compare simple and compound interest

About this lesson

Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Mathematics (MEL3E), expectation B3.4. It is a study resource, not an official curriculum publication.

Official curriculum reference

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