As student has $$5,000$ of which she does not want to consume in the current period. She is seeking an earning on the principal given that in $5$ years time she would take a holiday at which point she would liquidate her invested lump sum. A nearby savings company offers her the following options:Non$-$compounding return of $9\mathrm{.}5\%8\mathrm{.}25\%$ compounding annually$8\%$ compounding monthlya. Based on the the above investment options which of these will be the preferred option, where a higher future value is preferred to less. Rationalize your option' choice.b$.$ Prove that your option suggested in $"$a$"$above is correct by employing the effective annual rate $($EAR$)$ as we did in class and detailed in class notes.Answer text