$$Boy$,$ this is all so confusing,$$ said John as he stared at the papers on his desk. If only I had taken the advice of my finance instructor, I would not be in such a predicament today.$$ John Andrews aged $27,$ graduated five years ago with a degree in business administration and is

currently employed as a middle$-$level manager for a fairly successful grocery chain. His current salary of $$60,000$ has increased at an average rate of five percent per year and is projected to increase at least at that rate for the foreseeable future. The firm has had a voluntary retirement

savings program in place, whereby, employees can contribute up to $11\%$ of their gross salary $($up to a maximum of $$11,000$ per year$)$ and the company will match every dollar that the employee

contributes.

Unfortunately, like many other young people who start out in their first $$real$$ job, John has not taken advantage of the retirement savings program. He opted instead to buy a fancy car, rent an expensive apartment, and consume most of his income. However, with wedding plans on the horizon, John has finally come to the realization that he had better start putting away some money for the future. John$$s fianc$,$ Mary, of course, had a lot to do with giving him this realty check. Mary reminded John that besides retirement, there were various other large expenses that would be forthcoming and that it would be wise for him to design a comprehensive savings plan, keeping in mind the various approximate costs and timelines involved.

John figures that the two largest expenses down the road would be those related to the wedding and down payment on a house. He estimates that the wedding, which will take place in twelve

months, should cost about $$10,000$ in today$$s dollars. Furthermore, he plans to move into a $$200,000$ house $($in today$$s terms$)$ after five years, and would need $20\%$ for a down payment.

John is aware that his cost estimates are in current terms and would need to be adjusted for inflation. Moreover, he knows that an automatic payroll deduction is probably the best way to go since he is not a very disciplined investor.

John is not really sure how much money he should put away each month, given the inflation effects, the differences in timelines, and the salary increases that would be forthcoming. All this number crunching seems overwhelming and the objectives seem insurmountable. If only he had started planning and saving five years ago, his financial situation would have been so much better. But, as the saying goes, $$It$$s better late than NEVER!$4.$ John figures he will need approximately $$30,000$ per year $($in current dollars$)$ during his

retirement. If inflation is expected to average $4\%$ per year and John$$s savings yield $10\%$

per year, how long will his retirement savings last?

$5.$ How much would John have to save each month, starting from the end of the next month,

in order to accumulate enough money for his wedding expenses, assuming that his

investment fund is expected to yield a rate of return of $10\%$ per year?

$6.$ If John starts saving immediately for the down payment on his house, how much

additional money will he have to save each month? Assume an investment rate of return

of $10\%$ per year.

$7.$ If John wants to have a million dollars when he retires, how much should he save in equal

monthly deposits from the end of the next month? Ignore the cost of the wedding and the

down payment on the house. Assume his savings earn a rate of $8\%$ per year $($A$.$P$.$R$.)$

$8.$ If John saves up the million dollars by the time of his retirement at age $65,$ how much can

he withdraw each month in equal dollar amounts, if he figures he will live up to the age

of $85$ years? Assume that his investment fund yields a nominal rate of return of $8\%$ per