The idea, step by step
Create a fair comparison
Compare equal starting amounts over equal times. Convert rates to the appropriate periodic rates, calculate each final balance and then include the specified fees. A table helps keep each product rule separate.
A conclusion based on interest alone is conditional. Access to the money, risk, fees, changing rates and eligibility conditions may matter even when the arithmetic is correct. State which of these the supplied model includes.
Test a conclusion
Check whether a small change in a fee or assumed rate would reverse the result. This sensitivity check is more informative than reporting a long decimal answer.
Do not rank products invested for different periods by total dollars earned alone. Either use a common horizon or compare an annual growth measure with consistent assumptions.
A common trap
Different investment terms can be compared by interest dollars alone.
Instead: Use the same horizon, starting sum and cash-flow assumptions.
See the thinking
Worked example
For 3 years, compare AUD 8000 at 4.4% annual compounding with 4.3% nominal compounded quarterly. No fees.
- Annual model=8000(1.044)^3.
- Quarterly model=8000(1+0.043/4)^12.
- Use unrounded balances to decide which is larger.
Worked example
For one year, A pays 5% simple interest and no fee. B pays 5.5% simple interest and charges AUD 25. For what principal do their final amounts match?
- A=1.05 P;B=1.055 P−25.
- 0.005 P=25.
- P=5000; above this starting amount B gives more under these rules.
Check your understanding
An extra 0.4 percentage points of annual simple interest must cover AUD 20 fees. What principal breaks even?
Show answer
AUD 5,000.00
0.004 P=20 gives P=5000.
Your turn
6 questions · 12 marks · Work at your own pace.
Read the questions online
- Compare AUD 3000 for 2 years at 5% annual compound interest and 4.8% nominal compounded monthly. No fees.2 marks
- A AUD 2500 account earns 4% simple interest for one year and charges AUD 12. Find its final amount.2 marks
- For one year, A pays 3% simple interest/no fee; B pays 4% and charges AUD 18. Find the break-even starting amount.2 marks
- A model predicts A exceeds B by AUD 4 after 2 years. Explain why a possible AUD 10 closing fee matters.2 marks
- One account pays a fixed 4% for 2 years; another pays 5% only for the first year. Can a 2 year final comparison be determined?2 marks
- Compare 10% total growth over 2 years with 12% total growth over 3 years using annualised rates.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Compare AUD 3000 for 2 years at 5% annual compound interest and 4.8% nominal compounded monthly. No fees.2 marks
Evaluate 3000(1.05)^2 and 3000(1.004)^24.
Annual: AUD 3,307.50; monthly: AUD 3,301.64. - A AUD 2500 account earns 4% simple interest for one year and charges AUD 12. Find its final amount.2 marks
2500+100−12=2588.
AUD 2,588.00 - For one year, A pays 3% simple interest/no fee; B pays 4% and charges AUD 18. Find the break-even starting amount.2 marks
1.03 P=1.04 P−18.
P=18/0.01=1800.
AUD 1,800.00 - A model predicts A exceeds B by AUD 4 after 2 years. Explain why a possible AUD 10 closing fee matters.2 marks
If only A incurs the extra 10,its advantage becomes 4−10=−6.
It can reverse the ranking. - One account pays a fixed 4% for 2 years; another pays 5% only for the first year. Can a 2 year final comparison be determined?2 marks
A first-year promotional rate does not specify both years.
No; the second-year rate or balance rule is missing. - Compare 10% total growth over 2 years with 12% total growth over 3 years using annualised rates.2 marks
Annual factors are 1.10^(1/2) and 1.12^(1/3).
The two-year option has the higher annualised rate.
Two-year option: 4.881%; three-year option: 3.850%.
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 ↗