Let's solve this step-by-step:
1. Initial Value: The initial value of the car is [tex]$30,000.
2. Decay Rate: The car decreases in value by 20% each year.
3. Time Period: We need to find the value of the car after 4 years.
The formula to calculate the depreciated value of an asset, given an initial value, a decay rate, and a time period, is:
\[ V_f = V_i \times (1 - r)^t \]
where:
- \( V_f \) is the final value after the time period.
- \( V_i \) is the initial value.
- \( r \) is the decay rate.
- \( t \) is the time period.
Given:
- \( V_i = 30,000 \)
- \( r = 0.20 \)
- \( t = 4 \)
Let's substitute these values into the formula and calculate step-by-step.
1. First Year:
\[ V_1 = 30,000 \times (1 - 0.20) = 30,000 \times 0.80 = 24,000 \]
2. Second Year:
\[ V_2 = 24,000 \times (1 - 0.20) = 24,000 \times 0.80 = 19,200 \]
3. Third Year:
\[ V_3 = 19,200 \times (1 - 0.20) = 19,200 \times 0.80 = 15,360 \]
4. Fourth Year:
\[ V_4 = 15,360 \times (1 - 0.20) = 15,360 \times 0.80 = 12,288 \]
So, the resale value of the car after 4 years is $[/tex]12,288 when rounded to the nearest dollar.
