The idea, step by step
Read all the model choices
Check the rate convention, compounding interval, payment timing, fees, tax and rate changes. A fee-free model cannot be compared directly with one that includes fees without acknowledging the difference.
Use equal durations and starting contributions. A larger final balance alone does not prove a better return if the contributions differ.
Change one input at a time
Sensitivity testing recomputes a model after changing one input while holding the others fixed. It reveals dependence on assumptions, not a prediction of future account conditions.
Keep appropriate internal precision, check signs and domains, and round final currency as requested. For a long forecast, explain which assumptions might stop being reasonable.
A common trap
The largest headline percentage must produce the largest final balance.
Instead: Different fees, timing, conventions and contributions can reverse a comparison. Compare complete supplied models.
See the thinking
A fee affects later interest
Compare 1000 dollars at 5% annually over 2 years with no fee and with a 20-dollar fee at each year end.
- No fee gives .
- With fees: ; .
- The difference is 41 dollars: two fees and 1 dollar of lost interest on the first fee.
Rate sensitivity
Compare 2000 dollars over 2 years at annual compound rates of 4% and 5%.
- At 4%: .
- At 5%: .
- The difference is 41.80 dollars.
Check your understanding
A model predicts 1500 dollars before a 30-dollar fee charged only at the final time. Find the adjusted total.
Show answer
1470 dollars
Subtract the final fee once: 1500−30.
Your turn
6 questions · 15 marks · Work at your own pace.
Read the questions online
- A no-fee model gives 2640 dollars. A 25-dollar fee is charged only at the end. Find the adjusted result.2 marks
- Compare 1000 dollars compounded annually for 2 years at 3% and 4%. Find the difference.3 marks
- Why is comparing final balances unfair if one model starts at 500 dollars and the other at 1000 dollars?2 marks
- A calculation uses 5 instead of 0.05 as the decimal rate. What factor does it use instead of 1.05?2 marks
- A straight-line model gives an ordinary resale value of −80 dollars. What should be checked?3 marks
- State two assumptions in a 10-year model using a constant 6% annual compound factor with no other terms.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- A no-fee model gives 2640 dollars. A 25-dollar fee is charged only at the end. Find the adjusted result.2 marks
.
2615 dollars - Compare 1000 dollars compounded annually for 2 years at 3% and 4%. Find the difference.3 marks
.
20.70 dollars - Why is comparing final balances unfair if one model starts at 500 dollars and the other at 1000 dollars?2 marks
The larger starting amount alone may cause the larger final balance.
The initial contributions differ. - A calculation uses 5 instead of 0.05 as the decimal rate. What factor does it use instead of 1.05?2 marks
, which means a 500% increase.
6 - A straight-line model gives an ordinary resale value of −80 dollars. What should be checked?3 marks
Restrict or revise the model rather than accepting an uninterpreted negative value.
Whether the time lies outside the useful domain of the model. - State two assumptions in a 10-year model using a constant 6% annual compound factor with no other terms.3 marks
The expression contains only the principal and the same annual factor.
The rate stays 6%; there are no fees or extra transactions.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Simple versus compound growth; compound interest; depreciation; repeated percentage change; savings/loan scenarios with supplied models; changing assumptions and checking results; spreadsheets/digital models.
Official curriculum source ↗