Question

Irvin buys a car for ​$21 comma 804. It depreciates 25​% each year that he owns it. What is the depreciated value of the car after 1​ yr? after 2​ yr? The depreciated value of the car after 1 yr is ​$? The depreciated value of the car after 2 yr is ​$?

Answer 1

The depreciated value of the car after 1 yr is ​$16,353

The depreciated value of the car after 2 yr is ​$12,264.75

Explanation:

Given

purchase amount P= $21,804

rate of depreciation R= 25%

applying the formula for the car deprecation we have

`A= P*(1-(R)/(100) )^n`

Where,

A is the value of the car after n years,

P is the purchase amount,

R is the percentage rate of depreciation per annum,

n is the number of years after the purchase.

1. The depreciated value of the car after 1 yr is ​

n=1

`A= 21,804*(1-(25)/(100) )^1\\\\A= 21,804*(1-0.25 )^1\\\\A= 21,804*0.75\\\\A= 16353`

The depreciated value of the car after 1 yr is ​$16,353

2. The depreciated value of the car after 2 yr is ​

n=2

`A= 21,804*(1-(25)/(100) )^2\\\\A= 21,804*(1-0.25 )^2\\\\A= 21,804*0.75^2\\\\A= 21,804*0.5625\\\\A= 12264.75`

The depreciated value of the car after 2 yr is ​$12,264.75