Question

You buy a used car for \(\$ 7000\). The car depreciates at the rate of \(6 \%\) per year. Find the value of the car in the given years. 8 years

Short answer

The value of the car after 8 years is approximately \$4669.73.

Step-by-step solution

Identify the Variables

The original price of the car is \$7000. The annual depreciation rate is 6\% or 0.06 in decimal format.

Calculate Yearly Depreciation

To calculate the value of the car after each year, subtract the depreciation from the current value of the car. The formula to use is \(V = P * (1 - r)^n\), where \(V\) is the final value, \(P\) is the principal amount (initial amount), \(r\) is the rate of depreciation, and \(n\) is the number of time periods. Here, \(P = \$7000\), \(r = 0.06\), and \(n = 8\).

Find the Final Value of the Car

Substitute the given values into the formula and solve for \(V\). So, \(V = \$7000 * (1 - 0.06)^8 = \$4669.73\). The value of the car after 8 years is approximately \$4669.73.