Suppose a stock price can go up by $14\mathrm{.}75\%$ or down by $12\mathrm{.}75\%$ over the next year. You own a one$-$year put on the stock. The interest

rate is $11\%,$ and the current stock price is $$59.$

a$.$ What exercise price leaves you indifferent between holding the put or exercising it now? $($Do not round intermediate calculations.

Round your answer to $2$ decimal places.$)$

Break$-$even exercise price

b$.$ How does this break$-$even exercise price change if the interest rate is increased?

If the interest rate is increased, the value of the put option

decreases