Question

The value of a car after t years can be found using the formula V = C(1 - r)t, where V is the current value of the car, C is the original price of the car, and r is the rate of depreciation. Solve the formula for r . Raj bought a car 4.5 years ago for $25,000, and the current value of the car is $12,000. At what percentage rate has the car depreciated? Round your answer to the nearest whole number.

Answer 1

The given formula is
$V = C(1-r)^{t}$

Therefore
$(1-r)^{t} = \frac{V}{C} \\\\ 1-r = ( \frac{V}{C} )^{1/t} \\\\ r = 1 - ( \frac{V}{C} )^{1/t}$

Given:
C = $25,000
V = $12,000
t = 4.5 years

C/V = 0.48
1/t = 0.2222
Therefore
$r = 1 - 0.48^{0.2222} = 0.1505 = 15.05\%$

Answer: 15% (nearest integer)