Unit-cost depreciation
The amount lost depends on use, such as kilometres or operating hours
- Convert the quote Scale the quoted loss to one index block \(\displaystyle D=\frac{Cb}{q}\)
- Count index steps Divide total raw use u by the size of an index block \(\displaystyle n=u/b\)
- Calculate value Subtract n losses from the purchase price \(\displaystyle V_n=P-nD\)
- Reverse the calculation Find the total loss, divide by loss per step, then multiply by raw units per step
Worked example
A machine starts at $9,000 and loses $150 per 100 operating hours. The index counts 20-hour blocks. Find its value after 240 operating hours
- \(\displaystyle D=150\times20/100=30\)Each index step loses $30
- \(\displaystyle n=240/20=12\)There are twelve index steps
- \(\displaystyle V_{12}=9000-12\times30\)Subtract twelve losses
- \(\displaystyle V_{12}=8640\)The value is $8,640
Common mistakes
Quote mistaken for one raw unit
✕\(\displaystyle D=150\times20\)✓\(\displaystyle D=150\times20/100\)
The $150 loss is per 100 hours, not per hourTime mistaken for use
✕\(\displaystyle n=3\)✓\(\displaystyle n=u/b\)
Years are not usage blocks. Convert using the stated yearly use firstDifficulty levels
introIterate the supplied usage-block recurrence
standardRescale blocks and convert between use and value
challengeInclude yearly use and a different index block
examChoose value after a stated amount of use
Questions about this topic
Does n always mean years?+
No. Read its definition. It may count blocks of kilometres, hours, pages or other use
Why divide by the quoted block?+
It converts the quoted amount to loss per raw unit before scaling to the index block
Can different index blocks give the same value?+
Yes. For the same total use, changing block size changes the number of steps and loss per step together
Can I use a calculator?+
A calculator is allowed unless a question is marked no calculator
Which year level and chapter is this?+
Year 11, VCE Units 1 & 2, General Mathematics, chapter 3: Sequences and finance
In this chapter
Identify the behaviour of a sequenceFind the rule for a sequence and give the next term3A Sequence patterns and rules: Generate the terms of a sequence from a starting value and a rule3B Terms and recurrence relations: Generate the terms of a sequence from a starting value and a ruleName and number the terms of a sequence3B Terms and recurrence relations: Write a recurrence relation for a sequenceFind the common difference and the next term of an arithmetic sequenceDecide whether a sequence is arithmetic, geometric or neitherTabulate a sequence and graph its terms3D Arithmetic recurrence and terms: Write a recurrence relation for a sequenceFind term n of an arithmetic sequence using the rule3D Arithmetic recurrence and terms: Find when a sequence first reaches or passes a given valueModel a simple-interest investment or loan with a recurrence relationModel flat-rate depreciation with a recurrence relationModel unit-cost depreciation with a recurrence relationUse the rule for term n of a linear growth or decay modelRead the financial parameters out of a linear recurrence relation3E Linear growth and decay in finance: Find when a sequence first reaches or passes a given valueBuild and compare linear financial modelsFind the common ratio and the next term of a geometric sequenceTabulate and interpret discrete geometric graphsDistinguish arithmetic and geometric patternsWrite and interpret geometric recurrence rulesWrite an explicit geometric sequence ruleFind term n of a geometric sequence using the ruleFind the first geometric threshold index3H Compound interest and depreciation: Find when a sequence first reaches or passes a given valueModel a compound-interest investment or loan with a recurrence relationWrite a recurrence relation for a loan or investment with a given compounding periodConstruct complete compound-interest recurrence modelsFind the first financial threshold periodConstruct and use reducing-balance depreciation models3I Geometric models and finance: Find when a sequence first reaches or passes a given valueUse the rule for term n of a compound-interest or reducing-balance modelFind the interest on a credit-card debt compounding dailyCompare the total cost of ways of paying, or the return on ways of investingFind the effect of inflation on a priceFind the purchasing power of an amount after inflation