Having just graduated from Wayland with a degree in finance, you landed a job as a finance counselor for a large company. Your very first client is a young couple who want to put their financial business in order. Both the husband and the wife are $27$ years ago and in stable employment. They want to retire together at the age of $65.$ Thus, they have $38(=65-27)$ years until retirement from now. They want you to help them in their financial planning by answering a series of questions as follows.

$1.$ The couple has combined annual income of $$75,000$ today. They expect an annual average growth in their income of $4\%.$ Use Excel spread sheet to show your analysis. How much will they be making annually by the time they retire?

$2.$ They want to retire with $$2$ million in savings. They also want to set aside a flat $$5,000$ every year, at the beginning of each year starting now, as savings toward the retirement goal. What does the saving have to grow in value per year in order for them to achieve their retirement goal? They have no savings for this purpose as of today.

$3.$ Assume they have $$5,000$ already set aside for the purpose of retirement, how much would they have to save every year, at the beginning of each year starting now, in order to attain the goal of $$2$ million by the time they retire? Use Excel spread sheet to show your analysis. Assume they are able to achieve an average rate of return on their savings of $7\%.$

$4.$ If they have retired with $$2$ million in savings, and they want to withdraw $$100,000$ every year for living expenses at the beginning of each year, how long can their retirement nest egg last $($in years$)$ if the rate of return on their savings is $3\%$ post$-$retirement?

$5.$ The couple plan to have their first kid in exactly $2$ years from now. Today a college education costs about $$30,000$ a year. Assume this education cost grows with an annual inflation rate of $6\%.$ How much will the college education cost per year when the child turns $18?$