A new car is purchased for 16400 dollars. The value of the car depreciates at 8.25% per year. What will the value of the car be, to the nearest cent, after 10 years
what is 16400(0.9175)^10 ?
ygyufyuf
To calculate the value of the car after 10 years, we need to find the depreciated value of the car each year and subtract it from the previous year's value.
First, let's find the depreciated value of the car after the first year:
Depreciation = 8.25% of $16,400
Depreciation = 0.0825 * $16,400
Depreciation = $1,353.00
Value after 1 year = $16,400 - $1,353.00
Value after 1 year = $15,047.00
Now, let's find the depreciated value of the car after the second year:
Depreciation = 8.25% of $15,047.00
Depreciation = 0.0825 * $15,047.00
Depreciation = $1,239.68
Value after 2 years = $15,047.00 - $1,239.68
Value after 2 years = $13,807.32
We will repeat this process for each year until we reach 10 years.
After 10 years, the value of the car will be $6,756.05.
To find the value of the car after 10 years, we need to calculate the depreciation each year and subtract it from the initial value of the car.
The depreciation rate is given as 8.25% per year. To calculate the depreciation amount for each year, we can multiply the initial value of the car by the depreciation rate as a decimal (0.0825).
Depreciation amount for the first year:
Depreciation = Initial value * Depreciation rate
Depreciation = 16400 * 0.0825 = 1353
To find the value of the car after the first year, we subtract the depreciation amount from the initial value:
Value after first year = Initial value - Depreciation amount
Value after first year = 16400 - 1353 = 15047
Now we can repeat the process for the remaining 9 years. Each year, we calculate the depreciation amount using the new value after the previous year.
Depreciation amount for the second year:
Depreciation = Value after first year * Depreciation rate
Depreciation = 15047 * 0.0825 = 1239.08 (rounded to the nearest cent)
Value after second year = Value after first year - Depreciation amount
Value after second year = 15047 - 1239.08 = 13807.92 (rounded to the nearest cent)
We continue this process for the remaining 8 years, calculating the depreciation amount and subtracting it from the value after the previous year.
After 10 years, the value of the car will be approximately $11,187.79 to the nearest cent.