Better Late than Never

"Boy, this is all so confusing," said Jason 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." Jason Welch, aged $27,$ graduated five years ago with a degree in food marketing and is currently employed as a middle$-$level manager for a fairly successful grocery chain. His current annual salary of $$75,000$ has increased at an average rate of $5\%$ per year and is projected to increase at least at that rate for the foreseeable future. The firm has a voluntary retirement savings program in place, whereby employees are allowed to contribute up to $11\%$ of their gross annual salary $($up to a maximum of $$12,000$ per year$)$ and the company matches every dollar that the employee contributes. Unfortunately, like many other young people who start out in their first "real" job, Jason has not yet 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, Jason has finally come to the realization that he had better start putting away some money for the future. His fianc$,$ Jillian, of course, had a lot to do with giving him this reality check. Jillian reminded Jason 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 cost estimates and timelines involved.

$30$

Case $7,$ Better Late than Never

Jason figures that the two largest expenses down the road would be those related to the wedding and a down payment on a house. He estimates that the wedding, which will take place in $12$ months, should cost about $$22,000$ in today's dollars. Furthermore, he plans to move into a $$300,000$ house $($in today's terms$)$ after five years, and would need $20\%$ for a down payment. Jason 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 because he is not a very disciplined investor. Jason is really not 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!"

What was Jason's starting salary? How much could he have contributed to the voluntary savings plan in his first year of employment?

Had Jason taken advantage of the company's voluntary retirement plan up to the maximum every year for the past five years, how much money would he currently have accumulated in his retirement account, assuming a nominal rate of return of $7\%?$ How much more would his investment value have been worth had he opted for a higher risk alternative $($i$.$e$.,100\%$ in common stocks$),$ which was expected to yield an average compound rate of return of $12\%($A$.$P$.$R$)?$

If Jason starts his retirement savings plan from January of next year by contributing the maximum allowable amount into the firm's voluntary retirement savings program and continuing each year up until his retirement, how much money will he have accumulated for retirement, assuming he retires at age $65?$ Assume that the rate of return on the account is $7\%$ per year, compounded monthly and that the maximum allowable contribution does not change. Calculate the value of his retirement portfolio under, both, a monthly and an annual savings plan.

How much would Jason 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 $7\%$ per year?

If Jason starts saving immediately for the $20\%$ down payment on his house, how much additional money will he have to save each month? Assume an investment rate of return of $7\%$ per year.

If Jason wants to have a million dollars $($in terms of today's dollars$)$ when he retires at age $65,$ 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 $7\%$ per year $($A$.$P$.$R$.).$