A car is purchased for $17,500 . After each year, the resale value decreases by 20% . What will the resale value be after 5 years?

Question

Use a calculator and round to your nearest dollar

 

Answer 1

I calculated the value after 5 years to be 5,734.40 or 5,734 when rounded to the nearest dollar. Instead of reducing it by 20% each year, I calculated what 80% of the value would be. So, after 1 year the value is 0.80 times $17,500 or 14,000. I just continued to multiply the answer by 0.80 until I had done this 5 times.  

 

BTW....under this methodology after 10 years it would be worth about 1,879.05

 

...after about 20 years the value is approximately 201.76

Answer 2

Original Price = $17,500

 

if reduced by 20% each year,

after one year, this can be represented as:

 

$17,500 - 0.20*$17,500  or  $17,500*(1 - 0.2)  

 

or  $17,500*(0.8)

WE THEN JUST MULTIPLY THE PREVIOUS AMOUNT BY 0.8 EACH YEAR

 

making a table

YEAR     AMOUNT

   0        $17,500

   1        $17,500*(0.8)

   2        $17,500*(0.8)*(0.8)  

   3        $17,500*(0.8)*(0.8)*(0.8)    

and so on

 

WE CAN REWRITE THIS AS:  $17,500*(0.8)^N  WHERE N IS THE NUMBER OF YEARS

 

SO AFTER 5 YEARS:  AMOUNT = $17,500*(0.8)⁵  =  $5,734.40