Question

One model for car depreciation is as follows, where Cis the original cost, Vis the value of the car after tyears, and ris the rate
of depreciation
V= (1-1)
If the original cost of the car was $21,000 and the rate of depreciation is 15%, what will be the value of the car after 5 years?
[Round to the nearest dollar.]
A. $17,850
B. $3,150
C. $9,318
D. $19,472​

Answer 1

Given:

Original cost of car = $21000

Rate of depreciation = 15% = 0.15

Time = 5 years

To find:

The value of car after 5 years.

Solution:

Consider the model for car depreciation is

$V=C(1-r)^t$

where,  C is the original cost, V is the value of the car after t years, and r is the rate  of depreciation.

Substitute C=21000, r=0.15 and t=5 in the above model.

$V=21000(1-0.15)^5$

$V=21000(0.85)^5$

$V=21000(0.4437)$

$V=9317.7$

$V\approx 9318$

The value of car after 5 years is $9318. Therefore, the correct option is C.