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Ignition Learning — Activity Sheet

Loan repayments & amortisation

Mathematics · Year 12

Name: ______________________Date: ____________

A reducing balance loan charges interest on the current outstanding balance, which decreases with each repayment. An amortisation schedule breaks down each repayment into two parts: the interest portion (calculated on the remaining balance) and the principal portion (which reduces what's owed) — early in the loan, most of each payment goes toward interest, while later payments increasingly go toward the principal, since the balance (and therefore the interest charged) has shrunk.

Example

On a $10,000 loan at 6% annual interest with monthly repayments, an early monthly repayment of $200 might include $50 in interest and $150 reducing the principal, but by the loan's final months, that same $200 repayment might include only $2 in interest and $198 reducing the principal, since the outstanding balance is now much smaller.

Key terms

Reducing balance loan:
A loan where interest is charged on the current outstanding balance.
Amortisation schedule:
A table showing how each repayment splits between interest and principal.
Principal:
The original amount borrowed, or the remaining balance still owed.

Questions

  1. 1. A reducing balance loan charges interest on:

    • The current outstanding balance
    • Only the original amount, forever unchanged
    • A completely random amount each time
    • Nothing; reducing balance loans charge no interest
  2. 2. An amortisation schedule breaks down each repayment into:

    • Interest and principal portions
    • Only a single unified amount with no breakdown
    • Only fees, with no interest involved
    • Nothing measurable at all
  3. 3. Principal refers to:

    • The original amount borrowed or remaining balance owed
    • Only the interest charged
    • A type of fee unrelated to the loan amount
    • The lender's profit only
  4. 4. Early in a reducing balance loan, most of each payment goes toward:

    • Interest
    • Principal only, with no interest at all
    • Neither interest nor principal
    • A completely unrelated fee
  5. 5. Later in a reducing balance loan, more of each payment goes toward:

    • Reducing the principal
    • Interest only, with the principal untouched
    • Neither interest nor principal
    • A completely unrelated fee
  6. 6. As the outstanding balance shrinks, the interest charged:

    • Also shrinks
    • Always increases, regardless of balance
    • Stays exactly the same forever
    • Becomes completely unrelated to the balance
  7. 7. An amortisation schedule is presented as:

    • A table
    • A single number with no further detail
    • A type of graph with no numbers
    • A legal document with no financial data
  8. 8. On a $10,000 loan, an early $200 repayment splitting into $50 interest and $150 principal reduces the balance by:

    • $150
    • $200
    • $50
    • $10,000
  9. 9. If a later repayment includes only $2 interest and $198 principal, the total repayment amount is:

    • $200
    • $198
    • $2
    • $396
  10. 10. Why does the interest portion of each repayment shrink over the life of a reducing balance loan?

    • Interest is calculated on the outstanding balance, which decreases with each repayment made
    • Interest rates always decrease automatically over the life of every loan
    • The interest portion never actually changes throughout a loan's term
    • Repayment amounts always decrease to zero as a loan progresses
  11. 11. Why might making extra repayments early in a loan save more in total interest than making the same extra repayment later?

    • Reducing the principal earlier means less interest accumulates on that amount over the loan's remaining term
    • Extra repayments always save the exact same amount of interest regardless of timing
    • Interest calculations are completely unaffected by when extra repayments are made
    • Making extra repayments later in a loan always saves more interest than doing so early
  12. 12. Why might understanding an amortisation schedule help someone evaluate whether refinancing a loan makes financial sense?

    • It shows exactly how much of the current loan is interest versus principal, helping compare it to a new loan's terms
    • Amortisation schedules have no relevance to evaluating refinancing decisions
    • A loan's payment breakdown never changes throughout its term, making comparison unnecessary
    • Refinancing decisions are always made without any reference to interest and principal splits
  13. 13. Why might two loans with the same total repayment amount but different terms (e.g. 15 years vs 30 years) result in very different total interest paid?

    • A longer term means the balance remains outstanding for longer, allowing more interest to accumulate overall
    • Loan term length has no effect on the total interest paid over a loan's life
    • Both loans always result in identical total interest paid regardless of term length
    • A shorter loan term always results in more total interest paid, not less
  14. 14. Why might a borrower who understands amortisation be less surprised that their early repayments barely reduce the amount owed?

    • They would recognise that early repayments are weighted heavily toward interest rather than principal
    • Early repayments always reduce the principal by the full repayment amount
    • Amortisation has no bearing on how a borrower perceives their loan progress
    • Understanding amortisation always makes early loan progress feel faster than it is
  15. 15. Why might comparing the amortisation schedules of a reducing balance loan versus a flat-rate loan reveal significant cost differences?

    • A flat-rate loan charges interest on the original amount throughout, while reducing balance charges only on what remains owed, often making it cheaper overall
    • Reducing balance and flat-rate loans always result in identical total interest paid
    • Flat-rate loans always charge less total interest than reducing balance loans
    • The type of interest calculation used has no effect on total loan cost
  16. 16. A loan with a higher interest rate, all else being equal, will generally result in:

    • A larger interest portion in early repayments
    • A smaller interest portion in every repayment
    • No change to the interest portion of any repayment
    • A loan with no principal component at all
  17. 17. Why might a borrower choosing between a 5-year and a 10-year loan term for the same amount face a trade-off between monthly repayment size and total interest paid?

    • A shorter term means higher individual repayments but less time for interest to accumulate, while a longer term spreads cost but accrues more total interest
    • Loan term length never has any effect on either repayment size or total interest
    • A longer loan term always results in both lower repayments and lower total interest
    • Total interest paid is always identical regardless of the chosen loan term
  18. 18. Why might understanding amortisation help a borrower recognise the true cost of only ever making minimum repayments on a loan?

    • Minimum repayments may barely cover the interest, meaning the principal reduces very slowly and total interest paid over time can be very high
    • Minimum repayments always reduce the principal at the fastest possible rate
    • The size of a repayment never has any effect on how quickly a loan is paid off
    • Understanding amortisation has no practical connection to evaluating repayment strategies
  19. 19. Why might a lender require proof of income before approving a large reducing balance loan?

    • They need confidence the borrower can consistently make repayments, since a large portion of early payments is interest with slow principal reduction
    • Lenders never consider a borrower's ability to make repayments before approving a loan
    • Interest and principal repayment structure has no bearing on assessing loan risk
    • Proof of income is only ever relevant for loans with a flat interest rate, not reducing balance
  20. 20. Why might paying off a reducing balance loan slightly faster than scheduled (through occasional extra payments) meaningfully reduce total interest, even if the extra amounts are relatively small?

    • Any reduction to the principal earlier in the loan reduces the balance interest is calculated on for the remainder of the term
    • Extra payments only ever affect the very final repayment of a loan, with no earlier impact
    • The timing of extra payments has no bearing on total interest paid over a loan's life
    • Small extra payments never have any measurable effect on total interest paid
  21. 21. Why might comparing the total interest paid (not just the monthly repayment amount) be essential when comparing two different loan offers?

    • A lower monthly repayment can still result in significantly more total interest paid if the loan term is much longer
    • Monthly repayment amount always tells the complete story of a loan's true total cost
    • Total interest paid is always identical regardless of a loan's specific term or rate
    • Comparing total interest paid provides no additional useful information beyond monthly repayments

Answer key (parent copy)

  1. 1. The current outstanding balance
  2. 2. Interest and principal portions
  3. 3. The original amount borrowed or remaining balance owed
  4. 4. Interest
  5. 5. Reducing the principal
  6. 6. Also shrinks
  7. 7. A table
  8. 8. $150
  9. 9. $200
  10. 10. Interest is calculated on the outstanding balance, which decreases with each repayment made
  11. 11. Reducing the principal earlier means less interest accumulates on that amount over the loan's remaining term
  12. 12. It shows exactly how much of the current loan is interest versus principal, helping compare it to a new loan's terms
  13. 13. A longer term means the balance remains outstanding for longer, allowing more interest to accumulate overall
  14. 14. They would recognise that early repayments are weighted heavily toward interest rather than principal
  15. 15. A flat-rate loan charges interest on the original amount throughout, while reducing balance charges only on what remains owed, often making it cheaper overall
  16. 16. A larger interest portion in early repayments
  17. 17. A shorter term means higher individual repayments but less time for interest to accumulate, while a longer term spreads cost but accrues more total interest
  18. 18. Minimum repayments may barely cover the interest, meaning the principal reduces very slowly and total interest paid over time can be very high
  19. 19. They need confidence the borrower can consistently make repayments, since a large portion of early payments is interest with slow principal reduction
  20. 20. Any reduction to the principal earlier in the loan reduces the balance interest is calculated on for the remainder of the term
  21. 21. A lower monthly repayment can still result in significantly more total interest paid if the loan term is much longer