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You hear on the news that over the next 5
years, the inflation rate will skyrocket to
. If today a new Blu-ray movie costs
, assuming continuous
compounding, how much will that same
disk cost in 5 years?
Round your answer to the nearest cent (hundredth).

Ask by Gough Coles. in the United States
Jan 21,2025

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The Blu-ray movie will cost approximately $36.42 in 5 years.

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Extra Insights

To calculate the future cost of the Blu-ray movie considering an inflation rate of 12% compounded continuously, you can use the formula for continuous compounding:
where:
  • is the amount of money accumulated after n years, including interest,
  • is the principal amount (the initial amount of money),
  • is the annual interest rate (decimal),
  • is the number of years the money is invested or borrowed for,
  • is the base of the natural logarithm (approximately equal to 2.71828).
In this case:
Plugging in the values:
So, the cost of the Blu-ray movie in 5 years will be approximately $36.42.

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