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.
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.