You hear on the news that over the next 5 years, the inflation rate will skyrocket to \( 12 \% \). If today a new Blu-ray movie costs \( \$ 19.99 \), assuming continuous compounding, how much will that same disk cost in 5 years?

To calculate the future cost of the Blu-ray movie with continuous compounding at an inflation rate of \( 12\% \), we can use the formula: \[ A = Pe^{rt} \] where: - \( A \) is the amount of money accumulated after time \( t \), - \( P \) is the principal amount (the initial cost, which is \( 19.99 \)), - \( r \) is the annual interest rate (inflation rate, \( 0.12 \)), - \( t \) is the time in years (which is \( 5 \)), - \( e \) is the base of the natural logarithm (approximately equal to \( 2.71828 \)). Plugging in the values: \[ A = 19.99 \times e^{(0.12 \times 5)} \] Calculating \( e^{0.6} \) (since \( 0.12 \times 5 = 0.6 \)) gives approximately \( 1.8221 \). Now, multiply \( 19.99 \) by \( 1.8221 \): \[ A \approx 19.99 \times 1.8221 \approx 36.41 \] So, after 5 years, the Blu-ray movie that costs \( \$19.99 \) today will cost approximately \( \$36.41 \). Wait a minute, before you go rushing off to buy that disc, did you know that knowing how inflation works can help you plan your purchases better? You might want to snag that movie sooner rather than later! And if you're curious, exploring more about inflation can reveal just how it impacts everything from groceries to gas prices. Grab a book or a reliable online source—understanding your economy can be fun and eye-opening!