Jimmy and Jane Have Goals Jimmy Johnson is $25$ years old. He and his wife Jane, $27$ years old, have two children, Emmitt and

Patricia, ages $3$ and $5$ respectively. Jimmy wants to retire in $35$ 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 $35$ years would cost

$$325,000$ in today's prices. In forty years Jimmy also believes he and Patricia can live comfortably on $$60,000$ a year in today's

dollar terms. Realizing that retirement is only $35$ years away, and that they still have two children to raise and put through college,

Jimmy thought he had better start saving for their retirement dreams. Also, Patricia is only $13$ years away from college, and before

Patricia finishes, Emmitt will be ready for school in $15$ years. Currently Jimmy has $$20,000$ in an emergency money market account

earning $1\mathrm{.}5\%$ interest compounded daily. His desire is to never have to use those emergency funds and that they will become a part

of his estate. Jane and Jimmy also own their home that has a market value of $$275,000$ and a mortgage of $$175,000.$ The $3\mathrm{.}75\%$

mortgage has $27$ years remaining and the monthly payments are $$860$ for principal and interest. Jane is a health care professional

and earns an annual salary of $$65,000.$ Her employer puts an additional $$5,000$ each year into a $401(k)$ retirement plan. The

employer $401$k retirement amount currently has a balance of $$19,000$ and it is invested in a stock mutual fund, which has been

earning an annual rate of return of $8\mathrm{.}0\%.$ With the current level of the United States federal debt, Jane and Jimmy are not counting

on receiving any funds from social security at retirement. Jimmy is a stay$-$at$-$home dad and he regularly earns additional income

for the family as a carpenter, increasing his outside the home work as their financial plan dictates and his schedule and the economy

allows. With all of the concern about college tuition increasing over the years, Jimmy believes that the children will 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

$$6,000$ per year today, and the cost to attend a state school is $$18,000$ per year today. Inflation will have a great impact on Jane and

Jimmy's future retirement and college plans for their children. Based on what he has read and heard on the news, Jimmy believes

that inflation will average $3\mathrm{.}0\%$ per year for the next $35$ years; however, the cost of a college education will increase by $4\mathrm{.}0\%$ per

year for the junior college and state schools. Also, with the desirability of lakefront vacation homes, the house and property in

Georgia will probably increase at a rate of $5\mathrm{.}0\%$ per year, while his current home will increase in value at a rate of $3\mathrm{.}0\%$ per year.

Jane hopes and expects her annual salary will increase by at least $4\mathrm{.}0\%$ per year.

$8.(10$ points$)$ Assuming that at the date Jane retires, she wants enough income for $30$ years of retirement and the rate of inflation will remain at $2\mathrm{.}0\%$ per year, how much will Jimmy and Jane need to live on for the $30$ years? $($Hint: Use $$165,000$ for your payment variable.$)$

$9.(10$ points$)$ How much will Jimmy and Jane need to save per month to pay for their retirement income for $30$ years assuming that they can earn $7\mathrm{.}0\%$ per year, compounding monthly, on the invested funds. Assume Jimmy and Jane stop saving in $35$ years when they reach $60,$ and funds are then held in a savings account earning zero. Further, assume that the $401$k is NOT used for income, as it will be needed for a vacation home transition. $($Hint: Use $$6,500,000$ as your total future value variable.$)$