a new car is purchased for 22300 dollars. the value of the car deprecia…
11772.17 dollars
Question
a new car is purchased for 22300 dollars. the value of the car depreciates at 10.25% per year. what will the value of the car be, to the nearest cent, after 6 years?
Étapes de solution
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Understand the question
a new car is purchased for 22300 dollars. the value of the car depreciates at 10.25% per year. what will the value of the car be, to the nearest cent, after 6 years?
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Explanation
Step1: Define depreciation formula
The formula for exponential depreciation is $A = P(1 - r)^t$, where:
- $P = 22300$ (initial value),
- $r = 0.1025$ (annual depreciation rate),
- $t = 6$ (number of years).
Step2: Calculate $(1 - r)$
$1 - r = 1 - 0.1025 = 0.8975$
Step3: Compute $(0.8975)^6$
$0.8975^6 \approx 0.5279$
Step4: Find final value
$A = 22300 \times 0.5279 \approx 11772.17$
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Final answer
11772.17 dollars
Réponse
Explanation
Step1: Define depreciation formula
The formula for exponential depreciation is $A = P(1 - r)^t$, where:
- $P = 22300$ (initial value),
- $r = 0.1025$ (annual depreciation rate),
- $t = 6$ (number of years).
Step2: Calculate $(1 - r)$
$1 - r = 1 - 0.1025 = 0.8975$
Step3: Compute $(0.8975)^6$
$0.8975^6 \approx 0.5279$
Step4: Find final value
$A = 22300 \times 0.5279 \approx 11772.17$
Answer
11772.17 dollars
Question Image
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Subject
business
Sub Subject
finance
Education Level
high school
Difficulty
unspecified
Question Type
calculation
Multi Question
No
Question Count
1
Analysis Status
completed
Analyzed At
2026-02-09T20:32:55
OCR Text
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a new car is purchased for 22300 dollars. the value of the car depreciates at 10.25% per year. what will the value of the car be, to the nearest cent, after 6 years?
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