Consider a European put option on a stock index without dividends, with $1$ year to expiration and a strike price of $800.$ Suppose that the annual effective risk$-$free rate is $3\%$ and that the put costs $51\mathrm{.}66$ today. Calculate the price that the index must be in $1$ year so that being long in the put would be breakeven.

Consider a European put option on a stock index without dividends, with $1$ year to expiration and a strike price of $800.$ Suppose that the annual effective risk$-$free rate is $3\%$ and that the put costs $51\mathrm{.}66$ today. Calculate the price that the index must be in $1$ year so that being long in the put would be breakeven.

$747\mathrm{.}31$

$750\mathrm{.}46$

$746\mathrm{.}77$

$748\mathrm{.}52$

$745\mathrm{.}27$