a new car is purchased for 22300 dollars. the value of the car deprecia…

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?

Solution Steps

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?
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

$A = 22300 \times 0.5279 \approx 11772.17$
Final answer
11772.17 dollars

Answer

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

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Question Analysis

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

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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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