Question #89bbe

1 Answer
Apr 21, 2017

$17304.27

Explanation:

We must first realize that taking 2.75% off of something is the same as multiplying that thing by 0.9725, since after we remove 2.75% it is now worth 97.25% of its value.

If we remove 2.75% twice, it's the same as multiplying by 0.9725 twice, or multiplying by #0.9725^2#.

Now let's model the system here.

The car is initially worth 24865 (dollars, but I'll drop the sign for now). We then remove 2.75% every year for 13 years (2007-2020). As discussed above, that's equivalent to multiplying by #0.9725^13#.

The value of the car in the year 2020 will be:

#V=24865(0.9725)^13 = 17304.27#

Just for fun:

The value of the car in year "n" (this only makes sense for years after 2007) is:

#V(n)=24865(0.9725)^(n-2007)#