A truck was purchased for $134 000.
Using the reducing balance method, the value of the truck is depreciated by 8.5% each year.
Which one of the following recurrence relations could be used to determine the value of the truck after
CORE, FUR1 2019 VCAA 19 MC
Geoff purchased a computer for $4500. He will depreciate the value of his computer by a flat rate of 10% of the purchase price per annum.
A recurrence relation that Geoff can use to determine the value of the computer after
CORE, FUR2 2018 VCAA 5
After three years, Julie withdraws $14 000 from her account to purchase a car for her business.
For tax purposes, she plans to depreciate the value of her car using the reducing balance method.
The value of Julie’s car, in dollars, after
- For each of the first three years of reducing balance depreciation, the value of
is 0.85
What is the annual rate of depreciation in the value of the car during these three years? (1 mark)
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- For the next five years of reducing balance depreciation, the annual rate of depreciation in the value of the car is changed to 8.6%.
What is the value of the car eight years after it was purchased?
Round your answer to the nearest cent. (2 marks)
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CORE, FUR2 2017 VCAA 5
Alex is a mobile mechanic.
He uses a van to travel to his customers to repair their cars.
The value of Alex’s van is depreciated using the flat rate method of depreciation.
The value of the van, in dollars, after
- Recursion can be used to calculate the value of the van after two years.
Complete the calculations below by writing the appropriate numbers in the boxes provided. (2 marks)
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- By how many dollars is the value of the van depreciated each year? (1 mark)
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Calculate the annual flat rate of depreciation in the value of the van.
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Write your answer as a percentage. (1 mark)
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- By how many dollars is the value of the van depreciated each year? (1 mark)
- The value of Alex’s van could also be depreciated using the reducing balance method of depreciation.
- The value of the van, in dollars, after
years, , can be modelled by the recurrence relation shown below. At what annual percentage rate is the value of the van depreciated each year? (1 mark)
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b.i.
b.ii.
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CORE, FUR2 SM-Bank VCE 4
Damon runs a swim school.
The value of his pool pump is depreciated over time using flat rate depreciation.
Damon purchased the pool pump for $28 000 and its value in dollars after
- Write down calculations, using the recurrence relation, to find the pool pump's value after 3 years. (1 mark)
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- After how many years will the pump's depreciated value reduce to $7000? (1 mark)
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The reducing balance depreciation method can also be used by Damon.
Using this method, the value of the pump is depreciated by 15% each year.
A recursion relation that models its value in dollars after
- After how many years does the reducing balance method first give the pump a higher valuation than the flat rate method in part (a)? (2 marks)
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CORE, FUR2 SM-Bank VCE 3
Luke purchased a new pizza oven for his restaurant for $23 500.
He can depreciate the pizza oven using the reducing balance method at a rate of 12.5% per year.
- If
represents the value of the pizza oven after years, write a recurrence relation that models its value. (1 mark)
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- During what year will the pizza oven's value drop below $15 000? (1 mark)
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Luke has been advised that he can use flat rate depreciation at 10% of the purchase price.
- After 4 years, show which depreciation method gives the pizza oven the highest value? (1 mark)
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