Consider a one$-$period binomial model for a nondividend$-$paying stock. You are given the

following information:

a$.$ Each period length is $3$ months.

b$.$ The continuously compounded risk$-$free interest rate is $10\%.$

c$.$ An investor wishes to replicate a $3-$month European call option on the stock with a strike

price of $350.$

d$.$ The stock price at time $1$ will be either $450$ or $325.$

Calculate the amount the investor must lend at the risk$-$free rate.