Section $1$: Problem Statement

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 fiancee, 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 $401k,$ wedding and house accounts.

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 monih for the next $60$ months?