Answer:
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.
Step-by-step 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.
