Question

a car was valued at $41,000 in the year 2009 by 2013 the car value has depreciated to 19,000 if the car value continues to by the same percentage what will it be worth in 2019?

Answer 1

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:

$A=P(1-d)^n\\\\A=Value \ after \ n \ years\\P=Initial \ Value\\d=Rate \ of \ depreciation\\n=Time \ in \ years$

#We substitute for the years 2009-2013 to solve for d:

$A=P(1-d)^n\\\\19000=41000(1-d)^4\\\\0.475=(1-d)^4\\\\d=1-0.475^{0.25}\\\\d=0.1698$

#We then use the calculated depreciation rate above to solve for A after 10 yrs:

$A=P(1-d)^n\\\\=41000(1-0.1698)^{10}\\\\=\ 6,376.92$

Hence, the value of the car after 10 yrs is $6,376.92