Question

Jimmy and Jane Have Goals Jimmy Johnson is 25 years old. He and his wife Jane have two children, Emmitt and Patricia, ages 2 and 4 respectively. Jimmy wants to retire in 40 years and build boats. He would like a nice retirement home with some land on a peaceful lake in the mountains of Georgia. Jimmy believes that to purchase a home and lot in 40 years would cost $300,000 in today’s prices. In forty years Jimmy also believes he and Patricia can live comfortably on $50,000 a year in today's dollar terms. Realizing that retirement is only 40 years away, and that he still had two children to raise and put through college, Jimmy thought he had better start saving for his retirement dreams. Also, Patricia is only 14 years away from college, and before Patricia finishes, Emmitt will be ready for school in 16 years. Currently Jimmy has $25,000 in an emergency money market account earning 2.0% interest compounded daily. His desire is to never have to use those emergency funds and that they will become a part of his estate. He also owns his own home that has a market value of $225,000 and a mortgage of $150,000. The 5.0% mortgage has 27 years remaining and his monthly payments are $1126 for principal and interest alone. Jimmy’s annual salary is $60,000. His employer puts an additional $3,000 into a 401(k) retirement plan. This retirement amount currently equals $9,000 and it is invested in a stock mutual fund, which has been earning an annual rate of return of 8.0%.

With the current level of the federal debt, Jimmy is not counting on receiving any funds from social security at his retirement. With all of the concern about college tuition increasing over the years, Jimmy believes that the children will have to go to the local junior college for their first two years and then a state school for their last two years. The cost to attend the local junior college is $5,000 per year today, and the cost to attend a state school is $15,000 per year today. Inflation will have a great impact on Jimmy’s future retirement and college plans for his children. Based on what he has read and heard on the news, Jimmy believes that inflation will average 3.0% per year for the next 40 years; however, the cost of a college education will increase by 5.0% per year for the junior college and state schools. Also, with the desirability of vacation homes, the house and property in Georgia will probably increase at a rate of 5.0% per year, while his current home will increase in value at a rate of 3.0% per year. Jimmy hopes that his annual salary will increase by at least 4.0% per year. Note: For each of the computations completed below, answers can be stated to the nearest dollar.

Questions

7. (10 points) Assuming that Jimmy has no money set aside for his children’s college at this time, approximately how much will he have to save per month for Emmitt’s education, for Patricia’s education, if he earns 7.0% on the invested funds and the balance of education funds stays invested through the end of college. (Note that this question is a two-step process for each of Emmitt and Patricia’s education.)

8. (10 points) Assuming that at the date Jimmy retires, he wants enough income for 25 years of retirement and the rate of inflation will remain at 3.0% per year, how much will Jimmy and Jane need to live on for the 25 years? (Hint: Use $160,000 for your payment variable.)

9. (10 points) How much will Jimmy need to save per month to pay for Jane and his retirement income for 25 years assuming that Jimmy can earn 8.0% per year, compounding monthly, on the invested funds. Assume Jimmy and Jane stop saving in 40 years when they reach 65, and funds are then held in a savings account earning zero. Further, assume that the 401k is NOT used for income, as it will be needed for a vacation home transition. (Hint: Use $6,000,000 as your total future value variable.)

10. (10 points) Jimmy hopes that the money from his retirement funds plus what he makes on the sale of his current home when he is 65, will be enough to allow him to buy the retirement home. Can this goal be realized?

Answer 1

7.

Let amount to be saved per month for Emmitt's education = x for 16 years(192 months)

Monthly effective return on the invested fund = i = 1.07^1/12 - 1 = 0.00565415

Value of fund at the end of 16 years = x.{ (1+i)¹⁹²+(1+i)¹⁹¹+(1+i)¹⁹⁰+.........+(1+i)²+(1+i)}

= x.(1+i).{(1+i)¹⁹² - 1} / i (using formula for the sum of a G.P.)

= x.(1.00565415).{1.00565415¹⁹² - 1} / 0.00565415

= 347.2147.x

Present value of education cost at the end of 16 years is calculated as follows

t=0 corresponds to the end of 16th year

t	cost	discount factor	P.V.= cost.discount factor
0	5000.(1.05)16=10914.3728	1	10914.3728
1	5000.(1.05)17=11460.0916	1.07-1	10710.3660
2	15000.(1.05)18=36099.2885	1.07-2	31530.5166
3	15000.(1.05)19=37904.2529	1.07-3	30941.1612

Total 84096.4166

Therefore we must have 347.2147.x = 84096.4166  

or x = $242

Similarly, let amount to be saved per month for Patricia's education = y for 14 years(168 months)

Monthly effective return on the invested fund = i = 1.07^1/12 - 1 = 0.00565415

Value of fund at the end of 14 years = x.{ (1+i)¹⁶⁸+(1+i)¹⁶⁷+(1+i)¹⁶⁶+.........+(1+i)²+(1+i)}

= x.(1+i).{(1+i)¹⁶⁸ - 1} / i (using formula for the sum of a G.P.)

= x.(1.00565415).{1.00565415¹⁶⁸ - 1} / 0.00565415

= 280.7604.y

Present value of education cost at the end of 14 years is calculated as follows

t=0 corresponds to the end of 14th year

t	cost	discount factor	P.V.=cost.discount factor
0	5000.(1.05)14	1	9899.6580
1	5000.(1.05)15	1.07-1	9714.6177
2	15000.(1.05)16	1.07-2	28599.1081
3	15000.(1.05)17	1.07-3	28064.5453

Total 76277.9291

Therefore we must have 280.7604.y = 76277.9291

or y = $272