Answer :
Answer:
To determine the cost of the machine, we need to understand the depreciation pattern over the years. Assuming the depreciation follows a specific pattern, we can analyze the given information to find the initial cost or the pattern's details. However, without additional context, such as the initial cost or the depreciation rate, the problem is underdetermined. Here are a couple of possible interpretations and their solutions:Scenario 1: Constant Rate of DepreciationIf the depreciation is at a constant rate, we can calculate it using the given depreciations for the second and third years.Depreciation during the second year: $644Depreciation during the third year: $592.48This suggests a pattern where the amount of depreciation decreases each year. If the depreciation rate is constant, we can calculate the rate of decrease.[ \text{Depreciation rate between second and third year} = \frac{$592.48}{$644} ]Let's calculate this:[ \text{Depreciation rate} = \frac{592.48}{644} \approx 0.92 ]Scenario 2: Depreciation Pattern Based on PercentageIf the depreciation is based on a certain percentage each year, the cost of the machine decreases by a fixed percentage annually.Let's denote:( D_2 ) as the depreciation in the second year.( D_3 ) as the depreciation in the third year.Given: [ D_2 = 644 ] [ D_3 = 592.48 ]The relationship between these depreciations can be expressed if we assume a constant percentage decrease each year. Let ( r ) be the annual depreciation rate.[ D_3 = D_2 \times (1 - r) ] [ 592.48 = 644 \times (1 - r) ]Solving for ( r ):[ 1 - r = \frac{592.48}{644} ] [ r = 1 - \frac{592.48}{644} \approx 1 - 0.92 = 0.08 ]So, the annual depreciation rate is approximately 8%.Initial Cost of the MachineTo find the initial cost, we need more information such as the depreciation for the first year or the initial cost itself. Without that, we can't accurately determine the initial cost from the given data alone.If you have additional information, please provide it so we can refine the calculations. If not, we can use the depreciation pattern to estimate the initial cost assuming the depreciation follows a simple model.SummaryBased on the given data, the depreciation rate appears to be around 8%. However, to find the initial cost, additional information about the first year's depreciation or the initial cost is needed.
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