Financial math problem! please show all of the steps.

E1. Suppose the price of a security changes from period to period in such a manner that the price during period i is the price during period 1-1 multiplied either by u = 1.1 or by d = 1 /u, i 2 1. Suppose the price of the security in period 0 is 50. Aside from buying and selling the security, suppose one can also pay C in period 0 and receive either 100 in period 3 if the price in period 3 is at least 52, or 0 in period 3 if the price in that period is less than 52. Assuming an interest rate of r 0.05, determine C if no arbitrage is possible