The car will be worth less than $5000 in 9 years
How to determine the number of years?
The given parameters are:
- Rate, r = 20%
- Initial value, a = 30000
- Final value, L = 5000
The value of the car at year t is represented as:
L = a * (1 - r)^t
So, we have:
5000 = 30000 * (1 - 20%)^t
Divide both sides by 30000
0.167 = (0.8)^t
Take the natural logarithm of both sides
t ln(0.8) = ln(0.167)
Divide both sides by ln(0.8)
t = 8
Add 1 to the number of years, to get when it would be less than $5000
t = 9
Hence, the car will be worth less than $5000 in 9 years
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