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

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4 Answers

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
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.
 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.