Rebecca is interested in purchasing a European call on a hot new$$ stock, Up$,$ Inc. The call has a strike price of $$97$ and expires in $95$ days. The current price of Up stock is $$124\mathrm{.}47,$ and the stock has a standard deviation of $44\%$ per year. The$$ risk$-$free interest rate is $6\mathrm{.}53\%$ per year. Up stock pays no dividends. Use a$365-$day year.

a$.$ Using the$$ Black$-$Scholes formula, compute the price of the call.

b$.$ Use$$ put$-$call parity to compute the price of the put with the same strike and expiration date.

$$Note$$: Make sure to round all intermediate calculations to at least five decimal places.$$