A friend tells you he is interested in a market$-$linked GIC $($MLGIC$)$ offered by Canadian Bank of the Empire. This MLGIC has the following terms

$$It is a $3$ year non$-$redeemable product

$$A guaranteed return of $2\%$

$$It allows you to fully participate in the return $($price appreciation$)$ of the TSX $60$ index up to $13\%$

The current level of the TSX $60$ index is $950\mathrm{.}33.$ The index has a dividend yield of $1\mathrm{.}5\%$ and its volatility $($standard deviation of returns$)$ is $16\%.$

Canadian Bank of the Empire also offers a plain vanilla $3$ year non$-$redeemable GIC that pays $2\%$ p$.$a$.$ Assume a $$1,000$ investment and a risk free rate of $1\mathrm{.}1\%.$

a$.$ The$($plain vanilla OR MLGIC$)$ product dominates the$($MLGIC OR plain vanilla product$)$ by$\_\_\_\_\_\_$ dollars.$$

b$.$If the MLGIC had a $50\%$ participation rate $($that is you only got $50\%$ of the price appreciation over $2\%)$ and no maximum upside, the value of the MLGIC would be $\_\_\_\_\_\_\_\_$ dollars.