Problem $1(15$ marks$)$: You are considering the following $3$ investments, each with an upfront cost of $$90,000$ today. Which would you choose? Show your work to support your answer. a$)$ $$10,000$ at the end of each year for $15$ years with the first payment one year from today $($end of year $1).$ APR of $6\%$ with semi$-$annual compounding. $(5$ marks$)$ b$)$ $$10,400$ at the end of each year for $16$ years with the first payment $2$ years from today. APR of $7\%$ with annual compounding. $(4$ marks$)$ c$)$ $$8,800$ at the end of each year for $17$ years with the first payment one year from today $($end of year $1).$ APR of $5\%$ with monthly compounding. $(6$ mark