Answer:
The value of car after n years at the depreciation rate is $ 50,000
.
Step-by-step explanation:
Given as :
The cost of the car that Jill bought = $ 50,000
The depreciation rate of car value = r = 10 % a years
Let The car after n years of depreciation = $ A
Now, According to question
The cost of car after n years of depreciation = initial cost of car × ![(1 - \dfrac{\textrm rate}{100})^{\textrm time}](https://tex.z-dn.net/?f=%281%20-%20%5Cdfrac%7B%5Ctextrm%20rate%7D%7B100%7D%29%5E%7B%5Ctextrm%20time%7D)
Or, $ A = $50,000 × ![(1 - \dfrac{\textrm r}{100})^{\textrm n}](https://tex.z-dn.net/?f=%281%20-%20%5Cdfrac%7B%5Ctextrm%20r%7D%7B100%7D%29%5E%7B%5Ctextrm%20n%7D)
Or, $ A = $50,000 × ![(1 - \dfrac{\textrm 10}{100})^{\textrm n}](https://tex.z-dn.net/?f=%281%20-%20%5Cdfrac%7B%5Ctextrm%2010%7D%7B100%7D%29%5E%7B%5Ctextrm%20n%7D)
Or, $ A = $50,000 × ![(\frac{90}{100})^{n}](https://tex.z-dn.net/?f=%28%5Cfrac%7B90%7D%7B100%7D%29%5E%7Bn%7D)
I.e $ A = $50,000 × ![(0.9)^{n}](https://tex.z-dn.net/?f=%280.9%29%5E%7Bn%7D)
So, value of car after n years = $ 50,000 ![(0.9)^{n}](https://tex.z-dn.net/?f=%280.9%29%5E%7Bn%7D)
Hence The value of car after n years at the depreciation rate is $ 50,000
. Answer