Sure, let's go through the detailed, step-by-step solution for calculating how much the truck will be worth in three years given a certain rate of depreciation.
Merlin Devies buys a truck for \[tex]$528,000, and it depreciates in value by 15% each year. We need to calculate the value of the truck at the end of each of the next three years.
### Step-by-Step Solution:
1. Initial Value:
- The initial value of the truck is \$[/tex]528,000.
2. Depreciation Rate:
- The depreciation rate is 15% per year, which means each year the truck loses 15% of its remaining value.
3. Value after 1st year:
- At the end of the first year, the value of the truck will decrease by 15% of its initial value.
- Therefore, the truck’s value after 1 year is:
[tex]\[
\text{Value after 1st year} = \$528,000 \times (1 - 0.15) = \$528,000 \times 0.85 = \$448,800
\][/tex]
4. Value after 2nd year:
- At the end of the second year, the value of the truck will again decrease by 15% of its value after the first year.
- Therefore, the truck’s value after 2 years is:
[tex]\[
\text{Value after 2nd year} = \$448,800 \times (1 - 0.15) = \$448,800 \times 0.85 = \$381,480
\][/tex]
5. Value after 3rd year:
- At the end of the third year, the value of the truck will decrease by 15% of its value after the second year.
- Therefore, the truck’s value after 3 years is:
[tex]\[
\text{Value after 3rd year} = \$381,480 \times (1 - 0.15) = \$381,480 \times 0.85 = \$324,258
\][/tex]
So, after three years, the truck will be worth \[tex]$324,258.
### Answer:
The correct option is not explicitly listed in the given options, but the calculated value of the truck after three years is \$[/tex]324,258.
