Many financial advisors would suggest that you save early for your retirement. The reason is relatively few years of contributions to your retirement plan made early in your life are equivalent to many more years of contributions made later in your life. In order to understand this point better, we consider the following exercise. Suppose there are two investors: A and B. Both plan to retire after T years but save for their retirement in very different ways. Investor A puts $1 into his retirement account at the beginning of each year for T years (i.e., at t = 0, 1, . . . , T 1). Investor B does not make any contributions for the first N years, and try to make it up with more contributions at the start of each year for the remaining T N years, i.e., he will make contributions at t = N, N + 1, . . . , T 1.

(a) Suppose Investor B wants to have the same amount of money as Investor A when both of them retire. What is the annual contribution that Investor B has to make in the remaining T N years. Express your answer as a function of r, N and T.

(b) Suppose r = 0.02/year and T = 60 years. Plot the annual contribution that Investor B has to make in part (a) as a function of N for 0 N 40 years. Repeat the same exercise for r = 0.04/year and r = 0.06/year.