If an item is worth $12,000 at the start, loses 15% of its value in the first year and ends the second year at $9,180, its second-year depreciation rate is 10%. First find what it was worth at the start of the second year.
When depreciation is based on the value at the start of each year, the base changes. Write down the three values in order. Then compare the final two values to isolate the second year’s change.
- Multiply by the percentage remaining after the first year.
- Subtract the final value from the value after year one.
- Divide that loss by the value at the start of year two.
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Identify the base for each percentage
The first year starts at $12,000. The second year starts at the value after the first year. The wording ‘15% of its value at the start of the year’ tells you which amount represents 100%.
A loss of 15% leaves 85%. Using 0.85 as the multiplier gives the value remaining in one step.
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Worked example | Recover the second-year rate
After the first year, the item is worth $12,000 × 0.85 = $10,200. In the second year, it loses $10,200 − $9,180 = $1,020.
The second-year loss as a percentage of its starting value is $1,020 ÷ $10,200 × 100% = 10%. Check by multiplying $10,200 by 0.90 to recover $9,180.
The total two-year loss is $2,820 ÷ $12,000 × 100% = 23.5%. You can also multiply the remaining-value factors, 0.85 × 0.90 = 0.765. This shows that 76.5% of the original value remains.
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Practise with a different order of information
An item loses 20% of its value in the first year. Its value at the end of year two is 68% of the original value. Find the second-year depreciation rate.
Treat the original value as 100 units. After the first year, 80 units remain. After the second, 68 remain. The second-year loss is 12 units, and 12 ÷ 80 × 100% = 15%.
Check with multipliers. 0.80 × 0.85 = 0.68. Using a starting value of 100 units works here because all the given information is proportional to the original value.
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Frequently asked questions
Why can’t I subtract 15% from 23.5% to get the second rate?
The 8.5 percentage point difference expresses the second-year loss relative to the original value. The second-year rate uses the value at the start of year two.
What if both annual losses use the original value?
Calculate each loss from that same original value. The worked examples use the value at the start of each year, so read the base stated in the question.
Can the same method handle appreciation?
Yes. For an increase, subtract the earlier value from the later value and divide by the earlier value. A 10% increase gives a multiplier of 1.10.
Contents · Official syllabus and next practice
Official syllabus and next practice
Read the official SEAB 2027 syllabus
Try finding the first-year rate if the original and final values are unchanged and the second-year rate is given as 10%.