stocks in the health industry depreciated by 5.7% in the first eight months of 1993. Assuming that this trend were to continue, how much would a $70,000 investment be worth in 8 years? (Hint: 8 years corresponds to 12 eight-month periods. Round your answer to the nearest cent.)
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To calculate the future value of an investment with a given rate of depreciation over a certain period of time, we can use the formula:
Future Value = Initial Investment * (1 - Depreciation Rate)^Number of Periods
In this case, the initial investment is $70,000 and the depreciation rate is 5.7% or 0.057. We need to calculate the future value after 8 years, which corresponds to 12 eight-month periods.
Now, let's substitute the values into the formula:
Future Value = $70,000 * (1 - 0.057)^12
To get the answer, we can simplify the expression and round to the nearest cent.
Calculating the future value:
Future Value = $70,000 * (0.943)^12
Future Value = $70,000 * 0.58384
Future Value = $40,688.80
Therefore, a $70,000 investment in the health industry, assuming a 5.7% depreciation rate continuing for 8 years, would be worth approximately $40,688.80.