Questions: A vehicle purchased for 32500 depreciates at a rate of 8% per year. Determine the approximate value of the vehicle 12 years after purchase. Round to the nearest whole number.

A vehicle purchased for 32500 depreciates at a rate of 8% per year. Determine the approximate value of the vehicle 12 years after purchase. Round to the nearest whole number.

Transcript text: A vehicle purchased for $\$ 32500$ depreciates at a rate of $8 \%$ per year. Determine the approximate value of the vehicle 12 years after purchase. Round to the nearest whole number.

Solution

Solution Steps

Step 1: Understand the Problem

We are given the initial purchase price of an asset ($P$), its annual depreciation rate ($r$%), and the number of years ($t$) over which the depreciation is calculated. Our goal is to find the approximate value of the asset after $t$ years.

Step 2: Apply the Exponential Decay Formula

The future value ($V$) of the asset can be calculated using the formula: \[V = P \times (1 - \frac{r}{100})^t\] Substituting the given values: $P = 32500$, $r = 8$, and $t = 12$, we get: \[V = 32500 \times (1 - \frac{8}{100})^{12}\]

Step 3: Perform the Calculation

After performing the calculation, the future value of the asset is approximately $V = 11949$ when rounded to 0 decimal places.