John Smith graduated $5$ years ago, with a Business degree and an emphasis in Finance. John is currently employed as a Sr$.$ Financial Analyst in the Corporate Finance department of a multinational corporation. He has progressed well in his career, with the ultimate goal of becoming the company$$s CFO. John$$s current salary of $$78,000$ has increased at an average rate of $5\%$ per year, with routine merit raises, and he expects to continue doing so

John$$s firm, ABC Corporation, has a defined contribution plan $(401$k$)$ plan in place.

Employees are allowed to contribute up to $10\%$ of their gross annual salary $($up to a

maximum of $$10,000$ per year$)$ and the firm will match $50\%$ of the employee$$s

contribution. Unfortunately, John has not yet taken Professor Money Man$$s advice to

$$Save$,$ Start Young, and Pay Yourself First.$$ Instead, John has enjoyed his post$-$college, nice$-$salary life by leasing a new car, renting an apartment and going out to Player$$s every weekend. Now that he has wedding plans on the horizon, John has come to the realization $($with help from his fianc$$e$,$ Jane Doe$)$ that it$$s time to start saving $$ while he$$s still young!

John expects that the lovebirds$$ two largest future expenses will be the cost of a wedding $($short$-$term$),$ then later the down payment on a house $($medium$-$term$).$ The couple plans to spend $$10,000$ of their own money on the wedding in twelve months. They also hope to purchase a $$400,000$ house in $5$ years. Jane$$s parents have promised to match their $10\%$ down payment, but only if they manage to save it within $5$ years. Talk about motivation to save! Both future spouses agree that John will automate his savings by setting up monthly contributions to his $401$k$,$ wedding and house accounts.

PLEASE ANSWER ALL OF THE FOLLOWING

$1)$ If John Smith had fully taken advantage of his employer$$s $401$k plan and company

match, what would be his current $401$k balance based on his historical $($last five years$)$

salary and contributions? Assume that John made the maximum contribution every year, with a $6\%$ annual return compounded annually. Second part, what would be his current $401$k balance, had he taken more risk and achieved an annual return of $10\%?$

$2)$ You can$$t change the past. John will save better in the future. Assuming he starts in

January of next year $($at age $28)$ and contributes the maximum to his $401$k$,$ what will be his account balance at age $70(42$ years later$)?$ Second part, what if John decides to retire early at age $60(32$ years later$)$ what will be his account balance? For both calculations, assume an annual rate of return of $8\%,$ compounded annually.

$3)$ John$$s fianc$$e$,$ Jane Doe, is adamant about getting married in the next year. She is

insisting that John makes saving towards the $$10,000$ needed a top priority. John recalls that Professor Money Man says $$not to invest in long$-$term investments with short$-$term money.$$ Therefore, he plans to keep the wedding account in the bank and buy short$-$term $($under $1$ year maturity$)$ CD$$s$.$ Assuming John stays continuously invested in CD$$s yielding $2\%$ annual yield for the duration of each monthly deposit from the beginning month $($Month $0),$ how much will he have to contribute to the wedding fund every month for the next $12$ months?

$4)$ Jane does acknowledge that saving for a home down payment is not as big of a priority. But both future spouses agree that they should start putting money away towards the goal of $$40,000$ within five years. John recalls that a medium$-$term investing plan should not take as much risk, so he will plan to earn $4\%$ annually with a conservative strategy for their house fund. How much money will he have to save every month for the next $60$ months?

$5)$ Dreaming of early retirement at age $60,$ how much could John start withdrawing from his $401$k per month, if planning for a life expectancy of $85$ years? Assume a more moderate rate of return of $6\%$ annually, compounded annually, during his retirement years.