To solve this we are going to use the compounded interest formula: 
where
is the final value of the car after 
years
is the price of the car
is the rate in decimal form
is the number of times the rate is compounded per year
is the time in years
Part 1. Notice that since the car is losing 4.5% of its value semiannually, it is losing 9% annually; also the rate is going to be negative, so
. Since the car its value semiannually, 
. Also, to find , we are going to subtract 2005 from 2017: 
. Finally, we know for our problem that 
. Now that we have all the vales we need, lest replace them in our formula:
We can conclude that at the end of 2017 the char will be worth $14,903.68
Part 2. Since we want to know the year in which the price of the car will be zero,
. From our previous calculations we know that , 
,and . Lets replace those values in our formula one more time:
Since is the exponent, we are going to use logarithms to bring it down:
Since
cannot be evaluated (you can't divide by zero in mathematics), we can conclude that the value of the car will never be zero.
where
Part 1. Notice that since the car is losing 4.5% of its value semiannually, it is losing 9% annually; also the rate is going to be negative, so
We can conclude that at the end of 2017 the char will be worth $14,903.68
Part 2. Since we want to know the year in which the price of the car will be zero,
Since
Since