For each one-year period after a car was purchased, its value at the end of the year was 15% less than its value at the beginning of the year. If the value of the car 2 years after it was purchased is $17,918, what was the value of the car when it was purchased?

1 answer

Let's call the original value of the car "x".

After the first year, the car is worth 85% of its original value, or 0.85x.
After the second year, the car is worth 85% of its value after the first year, which is 0.85(0.85x) = 0.7225x.

We know that after two years, the car is worth $17,918:

0.7225x = $17,918

Solving for x:

x = $24,755

Therefore, the value of the car when it was purchased was $24,755.