Question

Tim has just had his 45th birthday. He has two children. One will go to college 4 years from now and require four year beginning of year payments for college expenses, $18,000, $19,500, $20,500, and $21,500. The other will go to college 9 years from now and require four year beginning of year payments for college expenses, $23,000, $23,500, $24,000, and $24,500. In addition, Tim plans to retire in 20 years. Tim wants to be able to withdraw $100,000 per year (at the end of each year) from an account for 25 years. The first withdraw occurs on his 61st birthday. What equal, annual, end –ofYyear amount must Tim save for each of the next 20 years to meet these goals if all savings earn a 8% annual rate of return?

Answer 1

The total Present Value of the cash outflows in the form of the children's college expense and Tim's retirement expenses should be equal to the total Present Value of Tim's year-end savings for the next 20 years. The discounting rate to be used is 8 %

PV of first child's college expenses = 18000 / (1.08)^(4) + 19500 / (1.08)^(5) + 20500 / (1.08)^(6) + 21500 / (1.08)^(7) = $ 51965.43

PV of second child's college expenses = 23000 / (1.08)^(9) + 23500 / (1.08)^(10) + 24000 / (1.08)^(11) + 24500 / (1.08)^(12) = $ 42413.25

PV of Retirement withdrawals = 100000 x (1/0.08) x [1-{1/(1.08)^(25)}] x 1/(1.08)^(15) = $ 336513.46

Total P of Cash Outflows = 336513.46 + 42413.25 + 51965.43 = $ 430892.14

Let the annual year-end savings be $ K

Therefore, 430892.14 = K x (1/0.08) x [1-{1/(1.08)^(20)}]

K = $ 43887.32 approximately.