Question

a vehicle purchased for 20 700 depreciates at a constant rate of 4%. Determine the approximate value of the vehicle 10 years after purchase​

Answer 1

Answer: Therefore, the approximate value of the vehicle 10 years after purchase is approximately $12,368.73.

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Explanation:

Given:

P = $20,700

R = 4% = 0.04

T = 10 years

Substituting the given values into the formula:

V = $20,700(1 - 0.04)^10

Calculating the value:

V = $20,700(0.96)^10

V ≈ $12,368.73

Therefore, the approximate value of the vehicle 10 years after purchase is approximately $12,368.73.

Answer 2

$13,762.04

Explanation:

To determine the approximate value of the vehicle 10 years after purchase, we need to calculate its depreciation over the given time period.

The vehicle depreciates at a constant rate of 4% per year.

This means that each year, the value of the vehicle decreases by 4% of its previous value.

To calculate the value of the vehicle after t years, we can use the formula:

`V=a(1-r)^t`

where:

• V is the value of the vehicle after t years.
• a is the initial value of the vehicle .
• r is the depreciation rate (in decimal form).
• t is the number of years.

In this case:

• a = $20,700
• r = 4% = 0.04
• t = 10 years

Substitute the values into the formula and solve for V:

`V=20700(1-0.04)^(10)`

`V=20700(0.96)^(10)`

`V=20700(0.6648326...)`

`V=13762.035565...`

`V=13762.04\;\sf(nearest\;hundredth)`

Therefore, the approximate value of the vehicle 10 years after purchase is $13,762.04.