Question

A new car is purchased for 15600 dollars. The value of the car depreciates at 12.25%

per year. To the nearest tenth of a year, how long will it be until the value of the car is
2700 dollars?

Answer 1

13.4 years exponential depreciation, because a car no matter how old should have some value. If I chose a linear depreciation, then it is possible for the car to have negative value, which is not realistic.

Explanation:

Your starting value is $15,600

Use the formula V = P *(1 - r*t)

Assuming the depreciation is linear instead of exponential.

$2,700 = $15,600*(1 - 0.1225*t)

solve for t.

2700/15600 = 1 - 0.1225*t

27/156 = 1 - 0.1225*t

0.1225 * t = 1 - 27/156

t = (1/0.1225) * (1 - 27/156)

t = (1/0.1225)* (129/156)

t = 6.7503924 years

Assuming an exponential depreciation:

V = P*( 1 - r)^t

$2,700 = $15,600 *(1 - 0.1225)^t

$2,700 = $15,600 *(0.8775)^t

2700/15600 = 0.8775^t

27/156 = 0.8775^t

ln (27/156) = ln (0.8775^t)

ln (27/156) = t* ln (0.8775)

-1.754019141 = t * -0.1306783236

t = -1.754019 / -0.130678323 = 13.42 years. ... if this was exponential depreciation.