HSC Mathematics Standard 2 · MS-F4/F5 · Annuities & Depreciation
Scenario AScenario B
Scenario A code:·
Straight-line: S = V₀ − DnDeclining-balance: S = V₀(1 − r)ⁿ
Scenario code:·
Class room
Class scenarios (newest first) — tap to load:
Partner challenge
Build a scenario in Scenario A — but your yearly budget is $10 000: contribution × payments per year must not exceed it (e.g. $10 000 annually, $5000 half-yearly, $2500 quarterly, $800 monthly — maxing the contribution slider forces annual payments; is that the best use of the budget?). Press Copy and give your partner the code — say it across the desk. (A is always yours; codes you load always arrive in B.)
Your partner loads your code into Scenario B, then builds their own Scenario A on the same budget to beat your final value. Rate and years stay as you set them — the winning move is how the money is split across the year.
Before pressing Load: predict whose scenario wins, and say why using the words
rate per period, number of periods, and contribution.
Set A and B to the same yearly total (e.g. $4200 half-yearly vs $8400 annually).
Which wins? This is what "compounding half-yearly" is worth.
Build a scenario. Press Copy and give your partner the code — say it across the desk. (This tab has one scenario — loading a code replaces your settings, so Copy yours first.)
Your partner loads your code, records the crossing year, then changes one setting to move the crossing as late as possible.
Before loading: predict which method gives the lower salvage value after 4 years, and say why using the words straight-line and declining-balance.
Find settings where the two curves never cross. What has to be true about the first year's loss under each method?