A strategy consists of buying a market index product at $$830$ and longing a put on the index with a strike of $$830.$ If the put premium is $$18\mathrm{.}00$ and interest rates are $0\mathrm{.}5\%$ per month, what is the profit or loss from the long index position by itself at expiration $($in $6$ months$)$ if the market index is $$840?$

Question $38$ options:

$$44\mathrm{.}90$ gain

$$34\mathrm{.}90$ gain

$$14\mathrm{.}90$ gain

$$5\mathrm{.}10$ gain

$$44\mathrm{.}90$ loss

$$34\mathrm{.}90$ loss

$$14\mathrm{.}90$ loss

$$5\mathrm{.}10$ loss