A video game costs \( \$ 60 \) today. It the inflation rate is \( 4.75 \% \) and is compounded continuously how much will this same video game cost in 5 years? Round your answer to the nearest cent (hundredth).

To calculate the future cost of the video game given continuous compounding, 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 price, in this case, \( \$60 \)), - \( r \) is the annual interest rate (inflation rate here, so \( 0.0475 \)), - \( t \) is the time in years (5 years), - \( e \) is the base of the natural logarithm (approximately \( 2.71828 \)). Substituting in the values: \[ A = 60 \times e^{(0.0475 \times 5)} \] Calculating: 1. Compute \( 0.0475 \times 5 = 0.2375 \). 2. Find \( e^{0.2375} \) which is approximately \( 1.2682 \). 3. Multiply \( 60 \times 1.2682 \approx 76.09 \). So, the video game will cost approximately **$76.09** in 5 years, rounded to the nearest cent.