A new car costs $30,000, The value decreases by 15% each year. How do you find the car's value after 4 years?

1 Answer
Oct 19, 2015

Answer:

After 4 years the car is worth #$15,660.19#

Explanation:

Let #a_1=30,000# be the car's initial value, We knwo, that every year the new value can be calculated as:

#a_{n+1}=a_n*(1-0.15)=0.85a_n#

From this we know, that the consecutive values form a (decreasing) geometric sequence with: #a_1=$30,000#, #q=0.85#, and every term #a_i# (for #i>=2#) is the car's value after year number #i-1#, so the value we are looking for is #a_5#

#a_5=a_1*q^(5-1)=a_1*q^4=30,000*(0.85)^4 ~~15,660.19#