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).

Question

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).

UpStudy AI · Accepted Answer

To find the cost of the Blu-ray movie in 5 years with continuous compounding, we can use the formula for continuous compounding:

$$ A = P \times e^{r \times t} $$

Where:
- $$ A $$ is the amount after time $$ t $$,
- $$ P $$ is the principal amount (initial cost),
- $$ r $$ is the annual interest rate (inflation rate),
- $$ t $$ is the time in years.

Given:
- Initial cost of the Blu-ray movie, $$ P = \$19.99 $$,
- Inflation rate, $$ r = 12\% = 0.12 $$,
- Time, $$ t = 5 $$ years.

Substitute the values into the formula:

$$ A = 19.99 \times e^{0.12 \times 5} $$

Now, we can calculate the cost of the Blu-ray movie in 5 years using continuous compounding.
Calculate the value by following steps:
- step0: Calculate:
  $$19.99e^{0.12\times 5}$$
- step1: Multiply the numbers:
  $$19.99e^{0.6}$$
- step2: Convert the expressions:
  $$19.99e^{\frac{3}{5}}$$
- step3: Convert the expressions:
  $$\frac{1999}{100}e^{\frac{3}{5}}$$
- step4: Multiply the numbers:
  $$\frac{1999e^{\frac{3}{5}}}{100}$$
- step5: Simplify:
  $$\frac{1999\sqrt[5]{e^{3}}}{100}$$
The cost of the Blu-ray movie in 5 years with continuous compounding is approximately $36.42. Rounding to the nearest cent, the cost will be $36.42.
The Blu-ray movie will cost approximately \$36.42 in 5 years.

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).

Upstudy AI Solution

Answer

Solution

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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).

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Economics Questions

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).