SOLUTION: Vanessa bought a car for $20,000 . It is expected to depreciate at a continuous rate. What will be the value of the car in 2 years? Use K

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Question 1025988: Vanessa bought a car for $20,000 . It is expected to depreciate at a continuous rate. What will be the value of the car in 2 years? Use K - .105. The answer should be $16,212.00 I think but I need to see the how or steps. Thanks.

Found 2 solutions by Alan3354, MathTherapy:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
Vanessa bought a car for $20,000 . It is expected to depreciate at a continuous rate. What will be the value of the car in 2 years? Use K - .105. The answer should be $16,212.00
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If K - .105 means it depreciates by 0.105 of its value per year:
After each year it's work 0.895 of the previous year (1 - 0.105)
--> 20,000*0.895 1st year
20,000*0.895*0.895 2nd year
=~ $16,020.50
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Oops, continuous depreciation.
Not usually used for cars.
Cars depreciate when a new model is released, often in September.
A 2014 Lexus becomes worth less in Sep 2015, then again in Sep 2016, etc.
My knowledge of cars' value caused me to miss the "continuous" depreciation mentioned.

Answer by MathTherapy(10552) (Show Source):
You can put this solution on YOUR website!
Vanessa bought a car for $20,000 . It is expected to depreciate at a continuous rate. What will be the value of the car in 2 years? Use K - .105. The answer should be $16,212.00 I think but I need to see the how or steps. Thanks.

Use the continuous compounding formula: , where:
A = Value in t years
P = Original value
e = 2.71828.......
r = rate of depreciation, which in this case, is: K = - .105
t = time in years
Therefore, becomes:

Depreciated value in 2 years, or

SOLUTION: Vanessa bought a car for $20,000 . It is expected to depreciate at a continuous rate. What will be the value of the car in 2 years? Use K - .105. The answer should be $16,212.00