An IRA is an investment vehicle available to most individuals to save for retirement. The benefit is that the interest is not taxed until you withdraw money, and most retirees are in a lower tax bracket than when they worked. Under current laws, the maximum annual contribution is \(\$ 5000\) until age 50 and \(\$ 6000\) thereafter, including the year one turns 50 . Suppose that you make the maximum contribution every year for 40 years, beginning at age 25 until age 65 .

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

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