A car is originally worth \$26\,300 and depreciates by \$2000 per year. Find the value of the car after 3 years.
A 2012 Holden Commodore is priced at \$33\,000 and depreciates by approximately \$4000 per year.
Complete the given table.
Using this depreciation method, state whether the car will ever be worth nothing.
Identify the depreciation method used in the calculations.
| \text{Year} | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| \text{Price } (\$) | 33\ 000 |
The spectator attendance at an annual sporting event was recorded for 4 consecutive years from its first year of running: 44\,500, 43\,800, 43\,100, 42\,400.
Find the decrease in attendance each year.
If the event attendance continues to decrease at the same annual rate, calculate the expected attendance in its fifth year.
It is estimated that a house purchased for \$254\,500 will depreciate by an average of \$9400 each year. Calculate:
The worth of the house after 1 year.
The expected worth of the house after 6 years.
The value of a fridge depreciates by a constant amount each year and is modelled by the recurrence relation:V_{n + 1} = V_{n} - 300 , V_{0} = 1600 Where V_{n} is the value of the fridge, in dollars, after n years. Construct a graph of the values for the first five years, including year 0.
A car is purchased for \$29\,000 and depreciates by \$1400 each year. The value of the car is modelled by:V_{n + 1} = V_{n} - 1400 , V_{0} = 29\,000
Where V_{n} is the value of the car, in dollars, after n years.
Find the value of the car after 1 year.
Find the value of the car after 5 years.
Find the total depreciation of the car after 5 years.
A motorbike purchased for \$5000 depreciates annually by \$300. The value of the motorbike is modelled by:V_{n + 1} = V_{n} - 300 , V_{0} = 5000 Where V_{n} is the value of the motorbike, in dollars, after n years.
Use the sequence facility on your calculator to find after how many years:
The value of the motorbike first drops below \$1000.
The motorbike will first lose more than half its value.
A new lounge suite depreciates by a constant amount each year and its value is modelled by the recurrence relation:V_{n + 1} = V_{n} - 700 , V_{0} = 4800 Where V_{n} is the value of the lounge suite, in dollars, after n years.
State the initial cost of the lounge suite.
State the amount of value lost each year.
A photocopier depreciates by a constant amount for every 100 pages printed. The value of the photocopier is modelled by the recurrence relation:V_{n + 1} = V_{n} - 14 , V_{0} = 2800 Where V_{n} is the value, in dollars, of the photocopier after n hundreds of pages printed.
State the initial value of the photocopier.
State the constant rate of depreciation.
Use the sequence facility of your calculator to find the value of the photocopier after 2400 copies have been made.
The firm using the photocopier will replace it with a new one when its value drops below \$2365. Find the number of copies that will have been made by the time the replacement happens.
There were 10\,100 digital sales of a particular song in its first month of release. The number of monthly digital sales decreased by 360 each month after.
The song registered 7580 digital sales in a particular month. State the decrease in the monthly sales from the first month.
State how many months after the initial month of release the song registered 7580 in monthly digital sales.
Production robots to be used in a car manufacturing plant were purchased for \$4\,455\,000. After 5 years, they depreciated to a value of \$4\,385\,000.
Calculate the annual depreciation using the straight-line method.
After 7 years, the robots are sold off. If they continue to depreciate at the same annual rate, find the price they can be sold for.
The graph shows the depreciation of a car's value, V_n in dollars, after n years.
State the initial value of the car.
State the depreciation of the car each year.
State the number of years when the car's value reaches \$14\,400.
Find the value of the car after 4 years.
A new car costs \$44\,000. It is estimated that the car will depreciate at \$4000 per annum. At the end of the depreciation period it is estimated that the car could be sold for \$32\,000.
Find the age of the car at the end of the given depreciation period.
Find the annual percentage rate of depreciation for the first year only. Round your answer to two decimal places.
A car was originally valued at \$33\,300 and depreciates by \$3000 per year.
Find the salvage value of the car after 4 years.
Find the percentage of the original value the car worth after 4 years. Round your answer to two decimal places.
Find the percentage of the original value that has been lost after 4 years. Round your answer to two decimal places.
A car originally worth \$37\,000 depreciates to \$10\,000 after 3 years.
State the total depreciation of the car.
Write this reduction as a percentage of the original price, correct to two decimal places.
Calculate the average annual amount of depreciation over these 3 years.
A TV depreciates at a constant rate each year. The value, in dollars, of the TV after n years is represented by the given graph:
State the initial value of the TV.
State the value of the TV that drop each year.
Write a recursive rule, V_{n + 1}, that gives the value of the TV after \left(n + 1\right) years.
A tablet depreciates at a constant rate each year. The value, in dollars, of the tablet after n years is represented by the given graph:
Write a recursive rule, V_{n + 1}, that gives the value of the tablet after \left(n + 1\right) years.
Find the number of years for the value of the tablet to be worth less than half of its initial value.
Find the number of years when the tablet is considered worthless.
A car is initially purchased for \$21\,000 and depreciates by \$1700 each year.
Write a recursive rule, V_{n + 1}, that gives the value of the car after \left(n + 1\right) years.
Use the sequence facility of your calculator to find the value of the car after 5 years.
Find the number years for the value of the car to first fall below \$12\,400.
A bobcat, initially purchased for \$70\,000, depreciates at a rate of \$12 for every day of use.
Write a recursive rule, V_{n + 1}, that gives the value of the bobcat after \left(n + 1\right) days of use.
Find the value that was lost over a five-week period, if the bobcat is used 6 days a week.
The owner of the bobcat will replace the tyres when the value drops below \$59\,209. Find the number of days of operation when he will first change the tyres.
A courier van, initially purchased for \$48\,000, depreciates at a rate of \$190 for every 1000 \text{ km} of use.
Write a recursive rule, V_{n + 1}, that gives the value of the van after \left(n + 1\right) thousand kilometres.
Use the sequence facility of your calculator to find the value of the van after it has travelled 12\,000 \text{ km}.
Use the sequence facility of your calculator to find after how many kilometres the van will first fall below \$47\,049 in value.
A stove currently selling for \$700 depreciates at 14\% per annum.
State the percentage of the original value that will remain after one year.
Hence, find the remaining value after one year.
Write a recursive rule, V_{n + 1}, that gives the value of the stove at the end of year \left(n + 1\right).
Use the sequence facility on your calculator to find the value of the stove after 8 years.
A television purchased for \$2600 depreciates at the rate of 18\% per annum.
Write a recursive rule, V_{n + 1}, that gives the value of the television at the end of year \left(n + 1\right).
Use the sequence facility on your calculator to find after how many years the television will first be worth less than 15\% of its original value.
Frank purchased a \$3100 laptop that depreciates at the rate of 16\% per annum.
Calculate the depreciation over the first year.
Hence, find the value of the laptop at the end of the first year.
Write a recursive rule, V_{n + 1}, that gives the value of the laptop at the end of year \left(n + 1\right).
Use the sequence facility on your calculator to find after how many years the laptop will be worth less than half its initial value.
A brand new car depreciates in value each year and its value is modelled by:V_{n + 1} = 0.89 V_{n} , V_{0} = 21\,000Where V_{n} is the value, in dollars, of the car after n years.
State the initial value of the car.
As a percentage, state the annual depreciation rate.
Use the sequence facility of your calculator to find the value of the car after 9 years.
When a car is worth less than \$700 it is deemed only useful for parts. Find after how many years the car is only useful for parts.
A brand new phone depreciates in value each year and its value is modelled by:V_{n + 1} = 0.77 V_{n} , V_{0} = 700 Where V_{n} is the value, in dollars, of the phone after n years.
State the initial value of the phone.
As a percentage, state the annual depreciation rate.
Use the sequence facility of your calculator to find the value of the phone after 3 years.
Katrina purchased this phone at the end of 2011. She will purchase a new phone once this phone has lost 45\% of its value. Find the year in which she will buy a new phone.
After one year, the value of a company’s machinery had decreased by \$10\,440 from \$87\,000. The value of the machinery depreciates by a constant percentage each year.
State the rate that the machinery depreciates by in the first year.
Find the value of the machinery at the end of the second year.
Write a recursive rule, V_{n + 1}, that gives the value of the machinery at the end of year \left(n + 1\right).
The company bought this machinery at the end of 2011. When the value of the machinery falls below \$6000, they will invest in new machinery. Find the year in which this will occur.
A motorbike depreciated in value from \$30\,000, when it was originally purchased, to \$14\,950 in 5 years.
The motorbike depreciated by a constant percentage, r, each year. Find r, rounding your answer to the nearest percent.
Hence, write a recursive rule, V_{\left(n + 1\right)}, that gives the value of the motorbike at the end of year \left(n + 1\right).
Use the sequence facility on your calculator to find after how many years the motorbike will first be worth less than 30\% of its original value.
Kenneth has been losing money on two of his share portfolios. The value of each portfolio n years after the beginning of 2013 is modelled by the following recurrence relations:
-
Portfolio A: A_{n+1} = 0.88 A_{n}, A_{0} = 43\,000
Portfolio B: B_{n+1} = 0.91 B_{n}, B_{0} = 29\,000
State the portfolio which was worth more at the beginning of 2013.
State the portfolio which was losing money more rapidly.
Use the sequence facility on your calculator to find the year in which the two portfolios will be worth the same amount.
Immediately following the global financial crisis James's share portfolio of \$310\,000 fell by:
-
6\% per month for the first 7 months
-
Then 9\% per month for the following 5 months
Write a recursive rule, V_{n + 1}, that gives the value of the portfolio \left(n + 1\right) months after the start of the financial crisis, where n \lt 7.
Calculate the value of his shares at the end of the 7 months.
Hence, write a recursive rule, V_{n + 1}, that gives the value of the portfolio at the end of month \left(n + 1\right), where V_{0} is the balance of James's share portfolio 7 months after the financial crisis.
Calculate the worth of his shares one year after the start of the financial crisis.
Before purchasing a car, Skye analyses the predicted depreciation rates of the two cars she is interested in:
Car A can be purchased for \$19\,000 and will depreciate by 12\% per year.
Car B can be purchased for \$22\,000 and will depreciate by 14\% per year.
Write a recursive rule, A_{n + 1}, that gives the value of car A at the end of \left(n+1\right) years.
Write a recursive rule, B_{n + 1}, that gives the value of car B at the end of \left(n+1\right) years.
Use the sequence facility of your calculator to find the value of car A after 6 years.
Use the sequence facility of your calculator to find the value of car B after 6 years.
If after 6 years she wants to sell her car and just wants to maximise the amount of revenue she receives from the sale, which car should she purchase?