Classroom · Years 9–10
Same percentage.
Different change.
A laptop starts at $1,000 and loses 10% of its remaining value each year. Does it lose $100 every year? Use the rows to explain your answer.
1. Predict, then investigate
| Period | Opening ($) | Change ($) | Closing ($) |
|---|
Arithmetic is carried without intermediate rounding; displayed amounts are rounded to cents. $ denotes illustrative dollars. No tax, fees, inflation or changing rates are modelled.
2. Keep the percentage; change the base
After a 10% decrease, 90% remains. The multiplier is 0.90. The starter goes from $1,000 to $900, then $810, then $729. The losses are $100, $90 and $81, because the same percentage is applied to a smaller value each year.
Declining value = starting value × (1 − r)n.
Growing value = starting value × (1 + r)n.
Here r is the percentage divided by 100, and n is the number of whole years. Choose “Growth” in the explorer to compare the opposite direction. These are constant-percentage models, not forecasts of actual asset prices.
A different model: straight-line depreciation
Subtracting 10% of the original $1,000 every year means subtracting a fixed $100. After three years the value is $700, not $729. The comparison line uses this fixed-dollar amount and stops at zero; this floor is a modelling choice, not a universal accounting rule.
3. Explain the change
- A $2,000 bicycle loses 20% of its remaining value each year. Find its value after two years and the dollar loss in each year.
- A price rises 10%, then falls 10%. Is it back where it started? Use $100 to test your answer.
- At a 100% annual decline, what happens after the first year? Why can this model never produce a negative asset value?
Reveal worked answers
- Year 1: $2,000 × 0.8 = $1,600, a $400 loss. Year 2: $1,600 × 0.8 = $1,280, a $320 loss.
- $100 × 1.10 × 0.90 = $99. The increase and decrease use different bases, so they do not cancel.
- The multiplier is zero, so the value becomes zero and stays there. A rate from 0% to 100% gives a multiplier from 1 to 0, never a negative multiplier.
Teaching notes and next steps
Ask students to distinguish a constant percentage from a constant dollar change. For senior extension, compare the two models and explain why the straight-line zero floor needs to be stated.
Designed around NSW Stage 5 MA5-FIN-C-02, including the declining-value formula. The straight-line comparison also offers an extension towards senior financial mathematics. Independent resource; no curriculum authority endorsement is claimed.
Next: regular savings and payment timing, or return to the compound interest investigation.