Sam, $30,$ earns $$60,000$ annually, expecting a $2\%$ salary increase yearly. His current job also includes a fully paid health insurance plan and right now he has no retirement savings. He recently inherited $$100,000$ and plans to save $5\%$ of his salary each year for retirement. He's paid bi$-$weekly but will invest his savings annually. Deposits will be made annually into an investment starting a year from now, with the last deposit at age $65$ when he plans to retire.

Sam is considering three investment options for maximizing his inheritance and salary savings for retirement:

a$.$ A low$-$risk money market fund by $$RTM Funds$$ with an expected annual return of $3\%.$

b$.$ A diversified fund named $$Bluewater fund$$ by $$Canada Mutual Fund$$ with a historical average growth rate of $10\%,$ although it carries significant risks. In past $10$ years, the returns have had a range from $2\%$ to $16\%.$

c$.$ An RRSP account, expected to yield an average annual return of $6\%,$ invested in a mix of Canadian government bonds, highly rated Canadian and U$.$S corporate bonds, and stocks of stable Canadian and U$.$S companies. The RRSP has lower volatility compared to the "Bluewater fund." In past $10$ years, the fund has generated returns as low as $4\%$ and as high as $8\%.$ Hence the return volatility of investing in the RRSP is less than that of the $$Bluewater fund$.$

Given the risk $/$ return characteristics of the different investment vehicles, Sam is currently evaluating the following investment options for retirement.

Option $1$: Invest the $$100,000$ in the money$-$market fund and allocate salary savings to the "Bluewater fund."

Option $2$: Invest the $$100,000$ in the money$-$market fund and allocate salary savings to the $"$RRSP fund."

Option $3$: Invest the $$100,000$ in the money$-$market fund, with half of salary savings in the $"$RRSP fund" and the other half in the "Bluewater fund."

Option $4$: He will invest the $$100,000($inheritance$)$ in the money$-$market fund $($today$).$ In addition, he will investment $30\%$ of his savings from the salary into the $$RRSP fund$$ and the rest in the $$Bluewater fund$.$

Sam is considering an alternative: pursuing an MBA using part of the inheritance. The program costs $$40,000,$ lasting $2$ years. Sam will pay the total cost upfront, starting the program today. Working part$-$time during the MBA, he will lose savings, requiring $$20,000$ from the inheritance to offset reduced earnings. Health insurance from the university, costing $$3,000$ annually, brings the total program cost to $$46,000.$ During the MBA, Sam won't invest the remaining inheritance due to unforeseen events.

After completing the MBA, Sam anticipes a potential promotion to a $$70,000$ salary in year three, growing at $3\%$ annually. If promoted, he plans to save $6\%$ of his salary, starting three years from now and continuing until age $65.$ The remaining inheritance will be invested three years from today, with an expected value of $$36,000$ accounting for interest in a savings account, assuming no unforeseen financial expenses occur.

Considering the MBA option and a three$-$year delay in retirement investments, Sam evaluates the following strategies:

Option $5$: Invest inheritance and salary savings in the "Bluewater fund" $($first deposit in three years$).$

Option $6$: Invest inheritance in the money$-$market fund $($three years from today$)$ and salary savings in the "Bluewater fund."

Option $7$: Invest inheritance in the "Bluewater fund" $($three years from today$).$ Allocate half of salary savings to the $"$RRSP fund" and the other half to the "Bluewater fund" $($first deposit in three years$).$

With a goal of a comfortable retirement for at least twenty years until age $85,$ Sam seeks the best savings strategy, considering retirees' feedback about CPP income not being sufficient after retirement.

$2.$ How much money Sam is expected to have under each option when he retires at the age of $65$ if he decides to pursue the MBA program?

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