A home stereo depreciates by 20% each year. What’s the value of a stereo, purchased new for $1,200, after two years?

Question

I need to know how to breakdown this equation. It's a multiple choice on a practice test and I am stuck on percentages. I did 1200x.40=480.00 but that is not one of my answer choices. Please give detailed help

Answer 1

This is a compound interest problem. The formula is:

 

A = P (1 + r/n)^(nt) where:

t is the time in years,

n is the number of times in each year interest is calculated,

r is the interest rate,

P is the original amount (Principal), and

A is the amount after t years.

 

In this case:

t = 2 years,
n = 1 time each year,
r = -20% = -0.2,
P = $1200, and
A = 1200 (1 - 0.2)^2

A = 1200 (0.8)^2

A = 1200 (0.64)

A = 12 * 64 = 640 + 128

A = $768

Answer 2

The stereo new was $1200.

The stereo depreciates 20% each year.

After the first year the stereo depreciates by 20%, or 1/5.

1/5 of $1200=$240

After the first year the stereo is worth $1200-$240=$960

After the second year the stereo, now worth only $960, depreciates another 20%, or 1/5.

1/5 of $960=$192

After the second year the stereo is worth $960-$192=$768.

$768/$1200=64% of its original value after two years

After the first year the stereo is worth only 80% of its original price.

After the second year the stereo is worth only 80% of 80% or 64% of its original price.

The value of the stereo after two years is $768.

Answer 3

Hi C;

100%-20%=80%=0.80

($1200)(0.80^x)

x=quantity of years

($1200)(0.80²)=$768

Answer 4

 1200 * ( 1- 0.20(2) )  = 1200( 0.60) =

                                    

                                  = 1200( 0.60) = 720

 

    So every year depreciates 20% , after 2 years depreciates 40 % , the value of stereo will reduce to

 

60% of its original value.