Question

Question #89bbe

Answer 1

$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)`