Question

Katelynn bought a used car and it was 5 years old. She purchased it for 10,250, after two years the Kelly Blue book value for her car is $8,075. Determine how much the car was worth when it was first bought by the original owners and determine what the depreciation rate is. Hint: Remember these are exponential equations of the form y=abx.

Answer 1

a) rate of depreciation is 11.24%

b) original price of car = $18605.33

Explanation:

The formula to apply is;

current price= original price *(1-r)^n where r is the rate of depreciation as a decimal and n is the time period

a) Find the rate of depreciation given that ;

The car was bought at $10,250 when it was 5 years old

After 2 years, the value was $8,075

Apply the formula ;

current price= original price *(1-r)^n

8,075=10,250* (1-r)²

8,075/10250 = (1-r)²

0.78780487804 =(1-r)²

√0.78780487804 =(1-r)

0.88758373016 = 1-r

r=1-0.88758373016

r=0.11241626983 ⇒ 11.24%

b) When the car was first bought, the price was;

Apply the formula;

current price= original price *(1-r)^n

10,250 =original price * (1-0.1124)⁵

10,250=O.P *(0.5509)

10,250/0.5509 = original price

$18605.33= original price