Question

A new car is purchased for 20300 dollars. The value of the car depreciates at 8.75% per year. What will the value of the car be, to the nearest cent, after 12 years?

Answer 1

To solve this problem, we will need to use the formula for exponential depreciation, which is V = P * (1 - r) ** t, where:

- V is the value of the item after a certain period of time,
- P is the initial purchase price of the item,
- r is the rate of depreciation per year, and
- t is the time (or number of years).

In this case, our initial purchase price P is $20,300, our rate of depreciation r is 8.75% (which we will use as 0.0875 in decimal form), and our time t is 12 years.

First, we need to calculate (1 - r), meaning we subtract our rate of depreciation from 1: 1 - 0.0875 = 0.9125.

Next, we take this result and raise it to the power of t (in this case, 12): 0.9125 ** 12 = approximately 0.3310281899.

Finally, we have to find the depreciating value of the car by multiplying our original purchase price P ($20,300) by the result of our previous calculation: $20,300 * 0.3310281899 = approximately $6,725.35.

Therefore, the car will be worth approximately $6,765.35 to the nearest cent, after 12 years, following a yearly depreciation rate of 8.75%.

Answer 2

The value of the car, to the nearest cent, after 12 years will be $ 6,765.35

Explanation:

Let's recall that depreciation on a car can be determined by the formula:

V = C * (1 - r)^t , where:

V is the value of the car after t years,

C is the original cost

r is the rate of depreciation

t is the number of years of utilization of the car

Therefore, we have:

V = C * (1-r)^t

V = 20,300 * (1 - 0.0875)¹²

V = 20,300 * 0.333268

V = 6,765.35 (rounding to the nearest cent)