A video game costs \( \$ 60 \) today. If the inflation rate is \( 4.75 \% \) and is compounde continuously how much will this same video game cost in 5 years?

To find the future cost of the video game, you can use the formula for continuous compounding: \( A = Pe^{rt} \), where \( A \) is the amount of money accumulated after time \( t \), \( P \) is the principal amount (initial cost), \( r \) is the rate of interest (inflation rate), and \( t \) is the time in years. Here, \( P = 60 \), \( r = 0.0475 \), and \( t = 5 \). Plugging in the values gives: \[ A = 60 e^{(0.0475 \times 5)} \] Calculating this, you get: \[ A \approx 60 e^{0.2375} \approx 60 \times 1.26824 \approx 76.09 \] So, the video game will cost approximately \( \$76.09 \) in 5 years. --- Did you know that inflation has been a common thread in economic history? The concept of inflation dates back to ancient Rome, where it was primarily driven by the devaluation of currency. Fast forward to today, and various measures of inflation help us understand the purchasing power of money over time! When dealing with future prices and inflation, it's always a good idea to check for common mistakes. One common pitfall is forgetting to convert the percentage rate into decimal form before calculations. Also, double-checking the time frame used in the equation can prevent costly errors when budgeting for future expenses!