Respuesta :
Answer : The value of car will be, $11477.0
Step-by-step explanation :
The original price of car = $23700
Rate of depreciation in the value of car = 13.5 % = 0.135
After one year, the price of car will be:
[tex]\$ 23700-(0.135\times \$ 23700)[/tex]
[tex]\$ 23700\times (1-0.135)[/tex]
[tex]\$ 23700\times (0.865)[/tex]
After 2 year, the price of car will be:
[tex]\$ 23700\times (0.865)\times (0.865)[/tex]
and so on.....
Thus, the formula will be:
[tex]\$ 23700\times (0.865)^n[/tex]
where,
'n' is the number of years
Here, n = 10
So,
[tex]\$ 23700\times (0.865)^5[/tex]
[tex]\$ 11477.01326\approx \$ 11477.0[/tex]
Thus, the value of car will be, $11477.0
The value of the car after 10 years is $5557.8.
What is depreciation?
Depreciation refers to the reduction in the value of an asset over time and such valued reductions are reflected in the Balance sheet at the year ended.
Given
A new car is purchased for 23700 dollars.
The value of the car depreciates at 13.5% per year.
According to the question,
The value of the car depreciates therefore the amount of the car is determined by the formula,
[tex]\rm Amount = P(1-\dfrac{r}{100})^t\\\\[/tex]
Where, P = $23700, r = 13.5% and t =10 years
Substitute all the values in the formula,
[tex]\rm Amount = P(1-{r})^t\\\\ \rm Amount = 23700(1-0.135)^{10}\\\\Amount=23700(0.865)^{10}\\\\Amount=23700\times 0.23\\\\Amount=5557.8[/tex]
Hence, the value of the car after 10 years is $5557.8.
To know more about Percentages click the link given below.
https://brainly.com/question/14675742
