Salaries usually grow at a rate around \( 2 \% \) annually. If your starting salary is \( \$ 41,600 \), how much would you be making after 40 years with the company? You may assume continuous compounding.

To determine your salary after 40 years with a continuous annual growth rate of \(2\%\), we can use the formula for continuous compounding: \[ A = P \times e^{rt} \] Where: - \(A\) is the amount of money accumulated after time \(t\), - \(P\) is the principal amount (initial salary), - \(r\) is the annual interest rate (growth rate), - \(t\) is the time the money is invested for, - \(e\) is the base of the natural logarithm (approximately \(2.71828\)). **Given:** - Starting salary, \(P = \$41,600\) - Annual growth rate, \(r = 0.02\) (2%) - Time, \(t = 40\) years **Plugging in the values:** \[ A = 41,600 \times e^{0.02 \times 40} = 41,600 \times e^{0.8} \] First, calculate \(e^{0.8}\): \[ e^{0.8} \approx 2.22554 \] Now, multiply this by the starting salary: \[ A \approx 41,600 \times 2.22554 \approx 91,750.50 \] **Final Answer:** After 40 years, your salary would be approximately **\$91,751**.