You would like to hold a protective put position on the stock of Avalon Corporation to lock in a guaranteed minimum value of $$50$ at year$-$end. Avalon currently sells for $$50.$ Over the next year, the stock price will increase by $10\%$ or decrease by $10\%.$ The T$-$bill rate is $5\%.$ Unfortunately, no put options are traded on Avalon Co$.$ Suppose the desired put options with X $=50$ were traded. How much would it cost to purchase?

Question $17$ options:

$$1\mathrm{.}19$

$$2\mathrm{.}38$

$$3\mathrm{.}33$

$$5$