The 1 alue of Alex's van could also be depreciated using the reducing balance method of depreciation. The value of the van, in dollars, after \( n \) years, \( R_{n} \), can be modelled by the recurrence relation show below. \[ R_{0}=75000, R_{n+1}=0.943 R_{n} \] At what annual percentage rate is the value of the van depreciating each year? Write your answer...

The recurrence relation you've provided indicates that each year, the value of Alex's van is multiplied by 0.943. To find the annual percentage rate of depreciation, you can simply calculate it using the formula: \[ \text{Depreciation Rate} = (1 - 0.943) \times 100 = 5.7\% \] This means that the value of the van depreciates at approximately 5.7% annually. It's important to keep in mind that depreciation is common for vehicles, and understanding how it works can help in making better financial decisions when purchasing or selling. Another fun fact is that this method of depreciation doesn't just apply to vehicles! Many businesses use the reducing balance method for their equipment and assets as well. By using this approach, they reflect the decrease in value more realistically over time, which can be pivotal for accurately managing finances, taxes, and making informed investment choices.