To find the value of the car after 12 years, we need to calculate the depreciation amount for each year and subtract it from the initial price of the car.
Depreciation rate = 13.75%
Initial price of the car = $20700
Depreciation amount for the first year = 13.75% of $20700 = 0.1375 * $20700 = $2844.75
Value of the car after the first year = $20700 - $2844.75 = $17855.25
Depreciation amount for the second year = 13.75% of $17855.25 = 0.1375 * $17855.25 = $2456.77
Value of the car after the second year = $17855.25 - $2456.77 = $15398.48
Following the same calculation method, we can find the value of the car after 12 years:
Value of the car after 12 years = $20700 - (sum of depreciation amount for 12 years)
Value of the car after 12 years = $20700 - ($2844.75 + $2456.77 + ... + depreciation amount for 12th year)
I can also help you find this value by doing the calculations, let me know if you would like me to proceed.
A new car is purchased for 20700 dollars. The value of the car depreciates at 13.75% per year. What will the value of the car be after 12 years?
3 answers
please proceed
Calculation of depreciation amount for each year and value of the car after each year:
1. Depreciation amount for the first year = 13.75% of $20700 = 0.1375 * $20700 = $2844.75
Value of the car after the first year = $20700 - $2844.75 = $17855.25
2. Depreciation amount for the second year = 13.75% of $17855.25 = 0.1375 * $17855.25 = $2456.77
Value of the car after the second year = $17855.25 - $2456.77 = $15398.48
3. Continue calculating the depreciation amount and value of the car for each subsequent year.
After 12 years, the value of the car will be:
Value of the car after 12 years = $20700 - (sum of depreciation amount for 12 years)
Value of the car after 12 years = $20700 - ($2844.75 + $2456.77 + ... + depreciation amount for 12th year)
Let's calculate the total depreciation amount for 12 years first:
Total depreciation amount for 12 years = $2844.75 + $2456.77 + ... (12 terms)
Total depreciation amount for 12 years = $20700 * (1- (1-0.1375)^12) / 0.1375
Total depreciation amount for 12 years = $20700 * (1- (1-0.1375)^12) / 0.1375
Total depreciation amount for 12 years ≈ $14531.36
Now, calculate the value of the car after 12 years:
Value of the car after 12 years = $20700 - $14531.36
Value of the car after 12 years ≈ $6168.64
Therefore, the value of the car after 12 years will be approximately $6168.64.
1. Depreciation amount for the first year = 13.75% of $20700 = 0.1375 * $20700 = $2844.75
Value of the car after the first year = $20700 - $2844.75 = $17855.25
2. Depreciation amount for the second year = 13.75% of $17855.25 = 0.1375 * $17855.25 = $2456.77
Value of the car after the second year = $17855.25 - $2456.77 = $15398.48
3. Continue calculating the depreciation amount and value of the car for each subsequent year.
After 12 years, the value of the car will be:
Value of the car after 12 years = $20700 - (sum of depreciation amount for 12 years)
Value of the car after 12 years = $20700 - ($2844.75 + $2456.77 + ... + depreciation amount for 12th year)
Let's calculate the total depreciation amount for 12 years first:
Total depreciation amount for 12 years = $2844.75 + $2456.77 + ... (12 terms)
Total depreciation amount for 12 years = $20700 * (1- (1-0.1375)^12) / 0.1375
Total depreciation amount for 12 years = $20700 * (1- (1-0.1375)^12) / 0.1375
Total depreciation amount for 12 years ≈ $14531.36
Now, calculate the value of the car after 12 years:
Value of the car after 12 years = $20700 - $14531.36
Value of the car after 12 years ≈ $6168.64
Therefore, the value of the car after 12 years will be approximately $6168.64.
2 answers