Assume that the premiums for European options on FST stock with $6$ months to expiration are given by:

where $K$ is an unknown strike price.

The continuously compounded risk$-$free rate is $5\%,$ and the market does not admit arbitrage opportunities. Suppose we simultaneously

enter today $($time $t=0)$ into the following two sets of transactions:

$($I$)$ Sell a $100-$strike call and buy a $100-$strike put

$($II$)$ Buy a K$-$strike call and selling a K$-$strike put

a$)$ Is $K>100$ or is Explain.

b$)$ Verify that the payoff of this combined position at expiration does not depend on the spot price of FST stock at expiration.

c$)$ By looking at the cashflow of this combined position today and the cashflow at expiration, what is the value of $K$ such that this position

has the same rate of return as the risk$-$free asset?