The value of car in 2004 is $14951, if Olivia purchased a car worth $18,000 in the year 2001 and it loses its value by 6% per year.
Step-by-step explanation:
The given is,
Car worth $18,000 in the year 2001
Loses its value by 6% per year
Step:1
Formula to calculate the worth of car with loss rate,
[tex]y = A(1-r)^{t}[/tex].....................................(1)
Where, y = Value of car after t period
A = Initial value of car
r = Loss rate
t = Time period
From give,
A = $18,000
r = 6 % per year
t = 3 years
Equation (1) becomes,
[tex]y = 18000(1-0.06)^{3}[/tex]
[tex]=18000(0.94)^{3}[/tex]
= (18000 × 0.830584)
= 14950.512
≅ 14951
Value of car in 2004, y = $14951
( or )
Step:1
t = 3 years ( 2001 to 2004 )
For 1st year,
= ( Worth of car in previous year ) -
( Worth of car in previous year × Loss rate )
= ( 18000 ) - ( 18000 × 0.06 )
= 18000 - 1080
= $16920
For 2nd year,
= ( 16920 ) - ( 16920 × 0.06 )
= 16920 -1015.2
= $15904.8
For 3rd year,
= ( 15904.8 ) - ( 15904.8 × 0.06 )
= 15904.8 - 954.288
= 14950.512
≅ $14951
Result:
The value of car in 2004 is $14951, if Olivia purchased a car worth $18,000 in the year 2001 and it loses its value by 6% per year.
