Question

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

Answer 1

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`