A 401k (and similar plans) is an investment vehicle available to most individuals to save for retirement. The benefit is that the investment is made before taxes (by payroll deduction), and interest is not taxed until the money is withdrawn. In theory, most retirees are in a lower tax bracket than when they worked. Under current laws (2016), the maximum annual contribution to all such plans in 2016 is $18,000 until age 50 and $24,000 thereafter, including the year one turns 50. Suppose that the maximum contribution is made every year for 40 years, beginning at age 25 until age 65.

Employers may match this contribution, but this is not considered here.

1. What is the future value of this retirement fund after 40 years, assuming an effective annual interest rate of 9%?

2. What effective annual interest rate is required for the future value of this investment to be $2 million after 40 years?