Your employer automatically puts 15 percent of your salary

Last updated: 8/6/2022

Your employer automatically puts 15 percent of your salary into a 401(k) retirement account at the beginning of each year. The account earns 9% interest (compounded continuously). Suppose you just got the job on January 1st, your starting salary is $35000, and you expect to receive a 3.5% raise at the end of each year. We denote by y(t) the value of your retirement account after t years. Your salary after t years is 35000 1.035. The balance on your retirement account at the beginning is y(0) = 5250. The differential equation modeling this situation is y' = Solving the initial-value problem gives the unique solution y(t) =