Consider a four$-$month call option on the British pound. The current exchange rate is $$/1\mathrm{.}6$ and the exercise price is $$/1\mathrm{.}6.$ The risk$-$ free rate on the $ is $8$ percent p$.$a$.,$ the risk$-$free rate on $$ is $11$ percent p$.$a$.,$ and the volatility of the spot rate $($and the forward rate$)$ is $10$ percent. You are a US investor. By translating the volatility into an up and down factor $($u and d$).$ solve the following problems:

a$)$ What is the value that you would be willing to pay for this American call option if you used the one$-$period binomial approach to value it$?$

b$)$ What would you be willing to pay for this option if the volatility were $14\mathrm{.}1$ percent?