Answer:
$6,376.92
Step-by-step explanation:
-Let d be the rate of depreciation per year.
-Therefore, the value after n years can be expressed as:
[tex]A=P(1-d)^n\\\\A=Value \ after \ n \ years\\P=Initial \ Value\\d=Rate \ of \ depreciation\\n=Time \ in \ years[/tex]
#We substitute for the years 2009-2013 to solve for d:
[tex]A=P(1-d)^n\\\\19000=41000(1-d)^4\\\\0.475=(1-d)^4\\\\d=1-0.475^{0.25}\\\\d=0.1698[/tex]
#We then use the calculated depreciation rate above to solve for A after 10 yrs:
[tex]A=P(1-d)^n\\\\=41000(1-0.1698)^{10}\\\\=\$6,376.92[/tex]
Hence, the value of the car after 10 yrs is $6,376.92
