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?
To find the value of the car after 10 years, we need to calculate the depreciation each year and subtract it from the original purchase price.
First, let's calculate the depreciation percentage for each year. The car depreciates at a rate of 8.25% per year, so we need to subtract 8.25% of the current value from it.
To calculate the value of the car after 1 year, we subtract 8.25% of $16,400 from it:
Depreciation for 1st year = 8.25% of $16,400 = 0.0825 * $16,400 = $1,353
The value of the car after 1 year would be $16,400 - $1,353 = $15,047.
To calculate the value of the car after 2 years, we repeat the process using the new value after 1 year as the starting point:
Depreciation for 2nd year = 8.25% of $15,047 = 0.0825 * $15,047 = $1,240
The value of the car after 2 years would be $15,047 - $1,240 = $13,807.
We continue this process for 10 years, calculating the depreciation and subtracting it from the current value each time.
Depreciation for 3rd year = 8.25% of $13,807 = 0.0825 * $13,807 = $1,140
Value after 3 years = $13,807 - $1,140 = $12,667
Depreciation for 4th year = 8.25% of $12,667 = 0.0825 * $12,667 = $1,045
Value after 4 years = $12,667 - $1,045 = $11,622
Depreciation for 5th year = 8.25% of $11,622 = 0.0825 * $11,622 = $958
Value after 5 years = $11,622 - $958 = $10,664
Depreciation for 6th year = 8.25% of $10,664 = 0.0825 * $10,664 = $879
Value after 6 years = $10,664 - $879 = $9,785
Depreciation for 7th year = 8.25% of $9,785 = 0.0825 * $9,785 = $807
Value after 7 years = $9,785 - $807 = $8,978
Depreciation for 8th year = 8.25% of $8,978 = 0.0825 * $8,978 = $741
Value after 8 years = $8,978 - $741 = $8,237
Depreciation for 9th year = 8.25% of $8,237 = 0.0825 * $8,237 = $680
Value after 9 years = $8,237 - $680 = $7,557
Depreciation for 10th year = 8.25% of $7,557 = 0.0825 * $7,557 = $623
Value after 10 years = $7,557 - $623 = $6,934
Therefore, the value of the car after 10 years will be approximately $6,934.
To find the value of the car after 10 years, we need to calculate the depreciation amount for each year and subtract it from the original value of the car.
Step 1: Calculate the depreciation amount for each year.
Depreciation rate = 8.25%
Depreciation amount = (Depreciation rate / 100) * Original value of the car
Depreciation amount for each year = (8.25 / 100) * 16400
Step 2: Calculate the value of the car after 10 years.
Value after 10 years = Original value of the car - (Depreciation amount for year 1 + Depreciation amount for year 2 + ... + Depreciation amount for year 10)
Value after 10 years = 16400 - [(8.25 / 100) * 16400 + (8.25 / 100) * 16400 + ... + (8.25 / 100) * 16400]
Value after 10 years = 16400 - (10 * (8.25 / 100) * 16400)
Value after 10 years = 16400 - (10 * (8.25 / 100) * 16400)
Value after 10 years = 16400 - (10 * 0.0825 * 16400)
Value after 10 years = 16400 - (10 * 1353)
Value after 10 years = 16400 - 13530
Value after 10 years = 2869.93
Therefore, the value of the car after 10 years, to the nearest cent, will be $2869.93.