Question

Alex purchased a new car for $28,000. The car's value depreciates 7.25% each year. What will be the value of the car 5 years after it is purchased? Round your answer to the nearest dollar.

Answer 1

Answer: $19,219 (rounded)

28,000 (0.9275)^5

Answer 2

Each year, you drop 7.25% from the current amount. (Leaving you with 92.25%)
To find the a percentage of something, multiply it as a decimal.
After one year, it would look like 28,000 × 0.9225.
Each year after, the amount is multiplied by 0.9225 again.
For five years, we multiply it by 0.9225 five times, the same as 0.9225^5.

$7.25\%=0.0725\\1-0.0725=0.9225\\\ 28,000\times0.9225^5\approx\boxed{\ 18706}$

The basic formula for depreciation is $p(1-r)^n$ where p is the principal (original/main) value, r is the rate as a decimal per unit of time n.