Understand the idea.
Read all the model choices
A complete financial model states its starting amount, duration, rate convention, compounding frequency and transaction timing. Include any fees, withdrawals, tax or rate changes that the question specifies; omitted assumptions can change a comparison.
Compare like with like. A larger ending balance can reflect larger deposits rather than more growth. Separate contributions and costs from interest, and hold the relevant starting conditions fixed when comparing two supplied rules.
Change one input at a time
Sensitivity testing changes one input while keeping the others fixed. Recalculate both results and compare them to show how strongly the conclusion depends on that assumption; the exercise does not predict future account conditions.
Check the first period, the direction of change and the units before trusting a longer forecast. Keep sufficient internal precision and round final currency as requested. State which fixed assumptions may become less plausible over a longer period.
See the method in action.
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.
Worked solution
- 1
Calculate the fee-free balance.
There are two annual compound periods and no withdrawals.
- 2
Calculate the first year with the fee.
The fee is charged after first-year interest.
- 3
Carry the reduced balance into year two.
Removing the first fee also reduces the amount earning second-year interest.
- 4
Explain the difference.
The difference includes two dollar fees and dollar of lost interest on the first fee.
1102.50 dollars versus 1061.50 dollars.
Rate sensitivity
Compare 2000 dollars over 2 years at annual compound rates of 4% and 5%.
Worked solution
- 1
Calculate the balance at four percent.
The same principal compounds for two years at the lower annual rate.
- 2
Calculate the balance at five percent.
Only the annual rate changes; principal, duration and compounding frequency stay fixed.
- 3
Compare the resulting balances.
A one-percentage-point rate increase raises this two-year model balance by dollars.
2163.20 dollars and 2205 dollars.
Try it yourself.
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 & reasoning
1470 dollars
The fee occurs once, only at the final time. Subtract it once from the predicted amount: dollars; no later interest adjustment is required.
Keep practising
6 worksheet questions · 15 marks
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 ↗