Starting today, all three open an investment account with $$2,000.$

Please answer the following questions for each person, Justin, Hema and Vanessa. Assume monthly compounding.Problem #$1$

Three $22$ year olds, Hema, Justin and Vanessa, have similar plans for the future. By the age of $37,$ they would all like to own a house or apartment. Each have started to save $$2,000$ towards this goal. They are in general agreement that the first step toward this goal is to accumulate a down payment of approximately $$100,000$ by the year $2037.$ They will reach there goals at different times, depending on how they spend, save and invest.

All three are fully employed by the same NYC financial services company and have similar compensation packages. They believe they have similar ideas and values when it come to savings, but their respective lifestyles reveal otherwise.

Justin does not spend much on clothing or foodie restaurants, but likes sports bars. He loves trading his own Robin Hood account. His portfolio is mostly short$-$term oriented because of high portfolio turnover. Most of his investment ideas come from REEDIT and Twitter Spaces. Technical analysis, with charts and lines, is the primary driver of his trades. All in all, not very good sources for trading ideas. In addition, Justin has a sports gambling account and loves fantasy football. When asked, he claims that he has a winning gambling record, but he cannot provide an accounting of his net wins$/$losses$.$ As a result of his investment style and propensity for gambling, his investment returns fall short of a buy and hold strategy with dollar cost averaging.

Hema has always been a diligent student and employee, but has trouble saving because of her social circle and lifestyle. First thing every morning includes a latte run. Evenings often end with appetizers and drinks with friends. All of her friends share the same lifestyle, but some receive an allowance from parents. Hema does not receive support. Her investment returns are slightly lower than market returns because she pays an annual fee of $1\mathrm{.}00\%$ to an investment advisor $($who apparently does NOT advise her on spending$/$saving habits.$)$

Vanessa loves to cook and spends most evenings at home with her partner. They split the rent and grocery bills. She loves coffee and avocado toast. Her guilty pleasures are an espresso machine and a cold brew system. Instead of going to Starbucks and spending $$6$ per latte, she grinds her own coffee and brews for $$\mathrm{.}50$ per drink. The investment style for Vanessa is a buy and hold, low fee strategy with $3$ ETFs and $12$ Individual stocks that she researches and discusses with family and friends.

Justin Hema Vanessa

Annual salary $$75,000$ $$82,000$ $$72,000$

Monthly take home $4,0004,4003,900$

Rent per month $2,8003,0001,800$

Sport betting losses per month $400--$

Dinning$/$Drinks out $350600150$

Morning latte $($$$6\mathrm{.}00)4216840$

Investment$/$savings per month $$408$ $$632$ $$1,910$

Investment return $($annual$)4\%8\%9\%$

Starting today, all three open an investment account with $$2,000.$

Please answer the following questions for each person, Justin, Hema and Vanessa. Assume monthly compounding.

In what year will each person have the $$100,000$ to purchase a residence? $($give detailed calculation $)$

Explain the long$-$term cash flow advantage that the first person to accumulate a down payment will have? $($requires thought; hint: transitioning from rent payments to mortgage payments$)$

What advice would you give Justin, Hema or Vanessa?