Declining balance

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Financial Maths - declining balance depreciation.
Test Yourself 1.

Future value.	1. A phone depreciates in value at a rate of 25% each year. A new Pixel 5 costs $999. What will be its value (to the nearest $10) after 3 years? Answer. Value = $420.
	2. Ben purchased a laptop for $3,200 and depreciated it using the declining-balance method at 20% p.a. How much (to the nearest $10) is the laptop worth 4 years after the purchase? Answer. Value = $1,310.
	3. A new start-up company purchases $132,000 worth of office equipment. The value of the furniture is depreciated using the declining balance method at a rate of 22.5% per annum. Calculate the value of the equipment after 5 years. Answer.Value = $36,904.76.
	4. A photocopier in an office is to be depreciated using the declining balance method. It was purchased new for $12,000 and depreciated by about $10,000 after 6 years of use. Which of the following graphs best shows the value of the photocopier over this period? Give reasons for your answer. Answer. (d).
	5. An asset is depreciated at 10% per half year using the declining balance method. The asset was originally purchased for $15,000. What is the salvage value of this asset (to the nearest dollar) after 4 years? Answer. $6,457.
Present value.	6. Ish purchased a Tablet to help with her Maths three years ago. It is now valued at $350 and it has depreciated using the declining balance method at the rate of 25% each year. How much did Ish pay (to the nearest dollar) for the Tablet originally? Answer. Original price: $830.
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Rate of depreciation.	11. Charles buys a car for $25,000. After 5 years, the value of his car - using the declining balance method - is $8,900. Calculate the percentage rate of depreciation on Charles' car (to one decimal place). Answer. Rate is 18.7%.
	12. Euan purchases some equipment for his business and wishes to depreciate its value over 6 years. He pays $43,600 for the equipment and after one year, the value depreciates to $36,188. (i) What is the percentage rate of depreciation of the equipment given the decrease in value after 1 year? (ii) What is the write-off value (to the nearest $) for Ewan's equipment at the end of 6 years? Answer.(i) Depreciation rate is 17% p.a. (ii) Write off value is $14,254.
	13. David is interested in buying a boat. He sees a boat he likes whose value is $38,000. He makes no decision but sees the same boat one year later. Its price is now down to $34,000 and the owner Miguel says the decrease is in line with its rate of depreciation. (i) What was the annual percentage rate of depreciation of the boat (to 1 decimal place)? (ii) What would David estimate the value of the boat to be one year later? (iii) What would David estimate the value the boat would have been 4 years before he first saw it? Answer.(i) Rate is 10.5%. (ii) Value following year is $28,220. (iii) Value 4 years ago was $80,070.
	14. A computer was purchased 3 years ago for $3,000. Its value has depreciated - using the declining balance method - so that its value is now $1,500. What is the rate of depreciation of the computer (to the nearest %). Answer.Rate = 26%.
Number of periods - Hint: use guess and check.	15. A PS4 console was purchased for $1400 a number of years ago. It is now valued at $400 after depreciating at a declining balance rate of 23% per year. Approximately how many years ago was the PS4 purchased? Answer. Purchased about 5 years ago.