Suppose a stock price can go up by $14\mathrm{.}50\%$ or down by $12\mathrm{.}50\%$ over the next year. You own a one$-$year put on the stock. The interest

rate is $12\%,$ and the current stock price is $$58.$

a$.$ What exercise price leaves you indifferent between holding the put or exercising it now?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

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