The value of a new $12,500 automobile decreases 20% per year. Find its value after 3 years.

Question

 This is a question from my Algebra 2 class homework. 

Answer 1

 

The formula is A = P( 1 - r )^t ... where A is the new amount, P is the principle, r is the decimal rate, and t is the time in years

 

      P = 12,500

      r = .2 ... the decimal equivalent of 20%

      t = 3  ... number of years

 

      Plugging these values into the equation, we obtain:

 

      A = 12,500(1 - .2)^3

      A = 12,500 (.8)^3

      A = 12,500 (.512)

      A = 6400

 

So after 3 years, the car will be worth $6400.

Answer 2

You should find out what 20% of $12,500 is first but multipying 12,500 by .2 which equals 2500; you would subtract that from the original price. So after the first year the car will be $10,000. (You could also multiply 12,500 by .8 to get 10,000). You could continue these steps twice more to get your answer.

 

The easiest may be use the .8 value three times: 12,500 x .8 = 10,000 x .8 = 8,000 x .8 = 6,4000.

 

At the end of the three years the car would cost 6,400.

 

I haven't tutored math in years, but I'm sure there's a formula that could make this even easier!