Problem 6. A stock index is currently selling at \\( S_{0}=23 \\). You have constructed an asymmetric butterfly spread on the stock index expiring in one year for the three strike prices \\[ K_{1}=20, K_{2}=24, K_{3}=26 \\] using call options for which you have purchased 4 calls at strike \\( K_{1}=20 \\). The effective annual interest rate is \4, meaning that \\( \\$ 1 \\) acrrues to \\( \\$ 1.04 \\) over a year. The cost of one call option on the stock index expiring in one year for the various strike prices are \\[ C(20)=4.83, C(24)=2.71, C(26)=1.97 \\] Draw the payoff and profit/loss diagrams for the butterfly spread. What are the breakeven stock index prices (i.e. the value of \\( S_{1} \\) for which the P\\&L for the butterfly spread is zereo)