Question

find the value of a 7 year old car if the purchase price was $25,000 and it depreciates at a rate of % per year15

Answer 1

Approximately $10,935.14.

Explanation:

The value of a car that depreciates at a rate of 15% per year can be calculated using the formula:

V=P(1−r)n

where:

V is the value of the car after n years,

P is the purchase price of the car,

r is the rate of depreciation, and

n is the number of years.

Given that the purchase price P is $25,000, the rate of depreciation r is 15% (or 0.15 as a decimal), and n is 7 years, we can substitute these values into the formula to find the value of the car after 7 years.

Let’s calculate:

V=$25,000(1−0.15)7

[assistant to=python code]–>

P = 25000 # purchase price in dollars

r = 0.15 # rate of depreciation

n = 7 # number of years

calculate the value of the car after n years

V = P * ((1 - r) ** n)

V

[assistant]–>

The value of the car after 7 years of depreciation at a rate of 15% per year is approximately $10,935.14.

Answer 2

$8010.43

Explanation:

To find the value of a 7-year-old car that depreciates at a rate of 15% per year, we can use the formula for exponential decay:

`\sf \textsf{Value} = \textsf{Initial Value} * (1 - \textsf{Rate})^{\textsf{Time}}`

In this formula:

• Initial Value is the purchase price of the car.
• Rate is the depreciation rate per year (expressed as a decimal).
• Time is the number of years.

In this case:

• Initial Value (
  `\sf \textsf{Purchase Price}`) = $25,000
• Rate of Depreciation = 15% or 0.15 (as a decimal)
• Time = 7 years

Substitute the known value in above formula:

`\sf \textsf{Value} = 25,000 * (1 - 0.15)^7`

Now, calculate this to find the value of the 7-year-old car:

`\sf \textsf{Value} = 25,000 * (0.85)^7`

`\sf \textsf{Value} \approx 25000 * 0.3205770883`

`\sf \textsf{Value} \approx 8014.427207`

`\sf \textsf{Value} \approx 8014.43 \textsf{ (in 2 d.p)}`

So, the estimated value of the 7-year-old car, given a depreciation rate of 15% per year, is approximately $8010.43 .