Suppose a bank offers you the following two year, non$-$cashable GICs $($i$.$e$.,$ withdrawals

are not allowed$).$ The first one pays a monthly rate of return $0\mathrm{.}35\%,$ the second one

pays a semi$-$annual rate of return of $2\mathrm{.}15\%$ and the third one a return of $4\%$ for the first

year and $4\mathrm{.}5\%$ for the second year. All interest payments are reinvested.

$($a$)$ Which investment would you prefer?

$($b$)$ Suppose now that the third GIC offers you the option to withdraw your investment

at a penalty of $1\%$ at the end of the first year. At what market interest rate for a

one year investment at the second year will you exercise this option?