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a certain car depreciates in value at the rate of 25% per year. if the original value of the car was $24,000 , what is the net change in the value of the car over a two-year period?

2007-06-18 16:18:50 · 5 answers · asked by mala 2 in Science & Mathematics Mathematics

5 answers

Value after 2 years = 24000 * (1 - 25/100)^2
= $24000 * 0.75^2
= $13500

Net change in value of the car is $24000-$13500=$10,500

2007-06-18 16:23:06 · answer #1 · answered by gudspeling 7 · 0 0

starting value = $24,000
After 1 year it has lost 25% of the value at the start of the 1st year. 25% of $24,000 is $6,000 so it is worth $18,000.
After the 2nd year it has lost 25% of the value at the start of the 2nd year. 25% of $18,000 is $4,500 so it is worth $13,500. The net change in value over 2 years is $24,000 - $13,500 = $10,500.
Note: the value after 1 year is 75% of the original value, and after 2 years is 75% of 75% of the original value The value after "n" years = $24,000 x (0.75^n)

2007-06-18 23:31:53 · answer #2 · answered by skipper 7 · 0 1

Since it loses 25% of its value, it KEEPS 75% each year.

So after one year, the car's value is
$24,000*0.75 = $18,000

After the second year, it is worth
$18,000*0.75 = $13,500

Since it started at $24,000, and ended at $13,500, the net change is
$24,000 - $13,500 = $10,500

I hope this helps!

2007-06-18 23:23:55 · answer #3 · answered by math guy 6 · 0 0

FV = PV(1 - i)^t
where
FV is future value
PV is present value
i is the rate of depreciation
t is time in years

FV = PV(1 - i)^t
FV = 24,000(1 - 0.25)^2
FV = 24,000(0.75)^2
FV = 24,000(0.5625)
FV = 13,500

After 2 years, the value of the car is $13,500.

net change = FV - PV
net change = 13,500 - 24,000
net change = -10,500

Answer: The net change over a two-year period is -$10,500.

The net change over a two-year period is a decrease of $10,500.

2007-06-18 23:33:06 · answer #4 · answered by mathjoe 3 · 0 0

After Year 1
Value = $24,000 - £6000 = $18,000

After Year 2
Value = $18,000 - $4,500
Value = $ 13,500

Change in value is $10,500

2007-06-19 12:11:56 · answer #5 · answered by Como 7 · 0 0

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