Question: Kelly and Brian Johnson are a recently married couple whose parents advised them to start saving immediately in order to have enough money down the road to pay for their retirement and their children’s college expenses. Today (t = 0) is their 25th birthday (the couple shares the same birthday).

The couple plan to have two children (Dick and Jane). Dick is expected to enter college 20 years from now (t = 20); Jane is expected to enter college 22 years from now (t = 22). So in years t = 22 and t = 23 there will be two children in college. Each child will take 4 years to complete college, and college costs are paid at the beginning of each year of college.

College costs per child will be as follows:

Year Cost per child Children in college

20 $58,045 Dick

21 62,108 Dick

22 66,456 Dick and Jane

23 71,108 Dick and Jane

24 76,086 Jane

25 81,411 Jane

Kelly and Brian plan to retire 40 years from now at age 65 (at t = 40). They plan to contribute $12,000 per year at the end of each year for the next 40 years into an investment account that earns 10% per year. This account will be used to pay for the college costs, and also to provide a nest egg for Kelly and Brian’s retirement at age 65. How big will Kelly and Brian’s nest egg (the balance of the investment account) be when they retire at age 65 (t = 40)?