QuestionJune 7, 2025

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

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

Solution
4.3(186 votes)

Answer

\76.11 Explanation 1. Identify the formula for continuous compounding Use the formula for continuous compounding: **A = Pe^{rt}**, where P is the principal amount, r is the rate, and t is time. 2. Substitute the given values Here, P = 60, r = 0.0475, and t = 5. Substitute these into the formula: A = 60e^{0.0475 \times 5}. 3. Calculate the exponent Compute 0.0475 \times 5 = 0.2375. 4. Evaluate the exponential function Calculate e^{0.2375} \approx 1.2685. 5. Calculate the final amount Multiply by the principal: A = 60 \times 1.2685 \approx 76.11.

Explanation

1. Identify the formula for continuous compounding<br /> Use the formula for continuous compounding: **$A = Pe^{rt}$**, where $P$ is the principal amount, $r$ is the rate, and $t$ is time.<br />2. Substitute the given values<br /> Here, $P = 60$, $r = 0.0475$, and $t = 5$. Substitute these into the formula: $A = 60e^{0.0475 \times 5}$.<br />3. Calculate the exponent<br /> Compute $0.0475 \times 5 = 0.2375$.<br />4. Evaluate the exponential function<br /> Calculate $e^{0.2375} \approx 1.2685$.<br />5. Calculate the final amount<br /> Multiply by the principal: $A = 60 \times 1.2685 \approx 76.11$.
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