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The general equation for depreciation is given by [tex][tex]$y=A(1-r)^t$[/tex][/tex], where [tex][tex]$y=$[/tex][/tex] current value, [tex][tex]$A=$[/tex][/tex] original cost, [tex][tex]$r=$[/tex][/tex] rate of depreciation, and [tex][tex]$t=$[/tex][/tex] time in years.

The original value of a car is [tex][tex]$\$[/tex]24,000[tex]$[/tex]. It depreciates [tex]15\%[/tex] annually. What is its value in 4 years?

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Sagot :

GinnyAnswer
Sure, let's walk through the step-by-step process to find the current value of the car after 4 years using the depreciation formula.

1. Identify the given values:
- Original cost, [tex]\( A = \$ 24,000 \)[/tex]
- Rate of depreciation, [tex]\( r = 15\% \)[/tex] or [tex]\( 0.15 \)[/tex] (converted to a decimal)
- Time, [tex]\( t = 4 \)[/tex] years

2. Write down the depreciation formula:
[tex]\[ y = A(1 - r)^t \][/tex]

3. Substitute the given values into the formula:
[tex]\[ y = 24000 \times (1 - 0.15)^4 \][/tex]

4. Calculate the term inside the parentheses:
[tex]\[ 1 - 0.15 = 0.85 \][/tex]

5. Raise the result to the power of 4:
[tex]\[ 0.85^4 \approx 0.52200625 \][/tex]

6. Multiply this result by the original cost:
[tex]\[ y = 24000 \times 0.52200625 \approx 12528.15 \][/tex]

Therefore, the value of the car after 4 years is approximately [tex]$\$[/tex] 12,528.15$.
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