The purpose of this exercise is to demonstrate that it is much more beneficial to begin to invest for retirement early than it is to wait. We will compare the investments of two investors, Alberto and Zachary. Alberto begins to invest immediately after graduating from college, whereas Zachary waits 10 years to begin investing. For the purposes of this demonstration, we will assume that the interest rate remains the same over the entire period of time.

(a) From age 25 to 35, Alberto invests $100 per month in an annuity that pays a 12% interest rate compounded monthly. Determine the accumulated amount in Alberto’s annuity after 10 years.

(b) At age 35, Alberto stops making monthly payments into his annuity, but he takes the money he accumulated in his annuity and invests it in a savings account with an interest rate of 12% compounded monthly. Using the compound interest formula A = p(1 + r/n)^{(n - t)}, determine the amount Alberto has in his savings account 30 years later when he retires at age 65.

(c) From age 35 to 65, Zachary invests $100 per month in an annuity that pays 12% interest compounded monthly. Determine the accumulated amount in Zachary’s annuity after 30 years.

(d) Determine the total amount Alberto invested during the 10 years from age 25 to 35.

(e) Determine the total amount Zachary invested during the 30 years from age 35 to 65.

(f)  Which investor has more money from the investments described here upon retirement?