Suppose you invest $10,000 in a 1–year–equity–linked–CD. At maturity, the CD is guar- anteed to pay the invested amount, plus 50% of the percentage gain (if any) during the year on the stock index to which it is linked. At the time you invest, the stock index is prices at $1,500. Your payoff in one year is $10,000×(1+c×C(S1,K,1))), where C(S1,K,1) is a one year call option on the index with strike price K, and c is a constant. Determine c and K. What would the value of the stock index have to be at the end of the year (at maturity of the CD) in order for the CD to pay you $12,000?