0

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

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

### 4 Answers by Expert Tutors

Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
5.0 5.0 (3 lesson ratings) (3)
0
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
Arthur D. | Effective Mathematics TutorEffective Mathematics Tutor
5.0 5.0 (6 lesson ratings) (6)
0
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.
Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
0
Hi C;
100%-20%=80%=0.80
(\$1200)(0.80x)
x=quantity of years
(\$1200)(0.802)=\$768
Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
0
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.