The current level of an equity index is $1364\mathrm{.}13$ and its future contract with $25$ days until maturity $(t=\frac{25}{250}=0\mathrm{.}10$ years$)$ trades at $1366\mathrm{.}70.$ The annual dividend yield of the index is $2\mathrm{.}1\%.$

Round to $2$ decimal places and enter without the percentage sign or the dollar sign $($e$.$g$.,10\mathrm{.}466\%$ would be entered as $10\mathrm{.}47,$$$5\mathrm{.}2963$ would be entered as $5\mathrm{.}30).$

a$)$ Find the annual risk$-$free rate implied by the spot$-$futures parity.

$\%$

b$)$ Assume that you can borrow or lend at $3\%$ annual, and an index fund is available to buy or sell. Devise a zero$-$net$-$investment trading strategy which will generate a guaranteed profit at the expiration date of the futures contract. Take contract size as $$1$ times the index value. Ignore fees, transaction costs, and margin requirements. What would be the profit per one unit of the futures contract?

$ $$

c$)$ Is this an arbitrage opportunity?

$($Click to select$)vv$