The idea, step by step
Track a reducing balance
For a simplified loan with periodic rate and repayment at each period end, the update is . Calculate interest first and then subtract the repayment because that is the supplied timing rule.
A repayment must exceed the period interest to reduce the balance that period. Keep full internal precision unless the contract model explicitly rounds each credit. A balance table makes the reduction visible.
| Month | Opening (AUD) | Interest (AUD) | Repayment (AUD) | Closing (AUD) |
|---|---|---|---|---|
| 1 | 1000.00 | 10.00 | 200.00 | 810.00 |
| 2 | 810.00 | 8.10 | 200.00 | 618.10 |
Compare two decisions
Borrowing now gives earlier access but usually adds finance costs. Saving first delays the purchase and may earn interest. Compare the complete payment totals, dates and assumptions; a higher cash price at the later date can also matter.
The lowest modelled cost is not a complete personal decision. State what the model leaves out, such as uncertain income, changing prices or the importance of access. Interpret the answer in the hypothetical situation instead of prescribing a real loan.
A common trap
Subtract the repayment before applying interest even when payment is at period end.
Instead: Follow the stated cash-flow order. End-of-period repayment follows that period’s interest calculation.
See the thinking
Worked example
A AUD 1000 loan charges 1% monthly. A AUD 200 repayment is made at each month end. Find the balances after months 1 and 2.
- B1=1000×1.01−200=810.
- B2=810×1.01−200=618.10.
Worked example
An item costs AUD 1500 now. Borrowing costs 18 monthly payments of AUD 90 and a AUD 30 fee. Saving first leads to a cash price of AUD 1560, paid entirely from savings. Compare purchase outlays.
- Borrowing=18×90+30=1650.
- Delayed cash outlay=1560.
- Difference=90;this does not value earlier use or other omitted factors.
Check your understanding
A AUD 2000 balance incurs 1% interest and a AUD 150 end-of-month payment. Find the new balance.
Show answer
AUD 1,870.00
2000×1.01−150=1870.
Your turn
6 questions · 12 marks · Work at your own pace.
Read the questions online
- Loan balance AUD 5000, monthly rate 0.6%, month-end payment AUD 250. Find the new balance.2 marks
- A AUD 10000 loan incurs 0.5% monthly interest. What is the interest in its first month?2 marks
- A AUD 10000 balance has 0.5% monthly interest and only AUD 40 repaid at month end. Does it fall? Find the new balance.2 marks
- Find the balance after 3 monthly periods on AUD 2000 at 1% per month with AUD 300 month-end payments.2 marks
- Cash price AUD 2200. A loan requires 24 payments of AUD 102 plus AUD 50 fee. Find the extra cost.2 marks
- A comparison assumes a constant loan rate and unchanged future cash price. Give two reasons its actual outcome could differ.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Loan balance AUD 5000, monthly rate 0.6%, month-end payment AUD 250. Find the new balance.2 marks
5000×1.006−250=4780.
AUD 4,780.00 - A AUD 10000 loan incurs 0.5% monthly interest. What is the interest in its first month?2 marks
10000×0.005=50.
AUD 50.00 - A AUD 10000 balance has 0.5% monthly interest and only AUD 40 repaid at month end. Does it fall? Find the new balance.2 marks
Interest=50.
10000+50−40=10010.
No; it rises to AUD 10010. - Find the balance after 3 monthly periods on AUD 2000 at 1% per month with AUD 300 month-end payments.2 marks
B1=1720.
B2=1437.20.
B3=1437.20×1.01−300=1151.572.
AUD 1,151.57 - Cash price AUD 2200. A loan requires 24 payments of AUD 102 plus AUD 50 fee. Find the extra cost.2 marks
24×102+50=2498.
2498−2200=298.
AUD 298.00 - A comparison assumes a constant loan rate and unchanged future cash price. Give two reasons its actual outcome could differ.2 marks
These variables are assumptions rather than guaranteed facts.
The loan rate could change; the future cash price could change.
Curriculum reference & lesson scope
SACE Board of South Australia
Stage 1 General Mathematics: investing and borrowing. Supplied educational models cover interest, investment comparisons, shares and credit; they are not recommendations of real products or statements of personal tax liability.
Official curriculum source ↗