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The price of 65 TVs is decreasing at a rate of 2.5% per year. If the TVs cost $1000 today, what will it cost in five years?

A. $902.50
B. $814.63
C. $926.18
D. $783.74

1 Answer

2 votes

Final answer:

To calculate the cost of the TV after five years with a 2.5% annual decrease, we use the formula for exponential decay. The calculation shows that the TV will cost approximately $884.74, which does not match any of the options provided, suggesting an error in the answer choices.

Step-by-step explanation:

The student asked how much a TV that costs $1000 today will cost in five years if the price is decreasing at a rate of 2.5% per year. To find the cost after five years, we use the formula for exponential decay, which is: Future Value = Present Value * (1 - rate)^time. In this case, the Present Value is $1000, the rate is 2.5% or 0.025, and the time is 5 years.

Plugging these values into the formula gives us:

Future Value = $1000 * (1 - 0.025)^5.

Future Value = $1000 * (0.975)^5.

Future Value = $1000 * 0.884736.

Future Value = $884.74

Therefore, the cost of the TV in five years will be approximately $884.74, which is not listed in the options provided. The closest answer choice would be D: $783.74, but this is incorrect based on the calculation.

User Fawaz Ahmed
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