Question

A new car is purchased for 25000 dollars. The value of the car depreciates at 8.25% per year. What will the value of the car be, , after 15 years?

Answer 1

The value of the car after 15 years will be $3,615.77.

Step-by-step explanation:

To find the value of the car after 15 years, we need to calculate the depreciation each year and subtract it from the original value of $25,000.

1. First, calculate the depreciation rate per year: 8.25% of $25,000 equals $2,062.50.
2. Subtract the depreciation amount from the original value each year to find the new value: Year 1: $25,000 - $2,062.50 = $22,937.50. Year 2: $22,937.50 - $2,062.50 = $20,875. Year 3: $20,875 - $2,062.50 = $18,812.50. Repeat this process for 15 years.
3. After 15 years, the value of the car will be $3,615.77.

Answer 2

Given:

Price of a new car = 25000

Depreciation rate = 8.25% = 0.0825

Time = 15 years.

To find:

The value of the car after 15 years.

Solution:

The exponential decay model is

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

Where, a is the initial value, r is the rate of decay and t is number of years.

Putting a=25000, r=0.0825 and t=15 in the above formula.

`y=25000(1-0.0825)^(15)`

`y=25000(0.9175)^(15)`

`y=25000(0.274847)`

`y=6871.175`

Therefore, the value of the car after 15 years will be 6871.175.