Aussie Maths & Science Teachers: Save your time with SmarterEd
Peter installed his new pool fence on 1 January 2013 at a cost of $12 000.
On 1 January of each year after 2013 its value is depreciated by 15% using the reducing balance method.
The value of the pool fence will be below $4000 for the first time on 1 January of what year? Show all working. (3 marks)
--- 5 WORK AREA LINES (style=lined) ---
`text{Test the values of different years using:}\ \ S=V_0(1-r)^n`
`S \text{(Jan17)} = 12\ 000(1-0.15)^4= 5000 xx 0.85^4= $2560`
`S \text{(Jan19)} = 12\ 000 xx 0.85^6= $4525.79`
`S \text{(Jan20)} = 12\ 000 xx 0.85^7= $3846.93`
`\text{2020 is the 1st year its value is below $4000 on 1 January.}`
`r=15% = 0.15`
`text{Test the values of different years using:}\ \ S=V_0(1-r)^n`
`S \text{(Jan17)} = 12\ 000(1-0.15)^4= 5000 xx 0.85^4= $2560`
`S \text{(Jan19)} = 12\ 000 xx 0.85^6= $4525.79`
`S \text{(Jan20)} = 12\ 000 xx 0.85^7= $3846.93`
`\text{2020 is the 1st year its value is below $4000 on 1 January.}`