Competitive Bank offers a $2-$year market$-$linked GIC. It has $100\%$ principal protection, a guaranteed minimum return of $1\mathrm{.}5\%$ and the potential for a higher, unlimited return tied to the performance of the S&P $500$ Index measured over the $2-$year period. The current level of the S&P Index is $$2,551,$ its annual standard deviation is $14\%$ and its dividend yield is $2\mathrm{.}5\%.$ As an alternative, Competitive Bank also offers a $2-$year standard, plain vanilla GIC with an annual return of $4\%.$ Assume a $$1,000$ investment and consider a risk$-$free rate of $1\mathrm{.}1\%.$

a$.$ What is the present value of the plain vanilla GIC?$$

b$.$ What is the present value of the minimum guaranteed return component of the market$-$linked GIC?

c$.$ What is the present value of the option embedded in the market$-$linked GIC?$$

d$.$ What can you conclude about the value of the market$-$linked GIC compared to that of the plain vanilla GIC?

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