Problem $3$ You are given:

The current price of a stock is $$65.$

One year from now the stock will sell for either $$60$ or $$70.$

The stock pays dividends continuously at a rate proportional to its price. The dividend

yield is $4\%.$

The continuously compounded risk$-$free interest rate is $6\%.$

The current price of a one$-$year $65-75$ European put bear spread on the above stock is

$$6\mathrm{.}50.$

Describe transactions $($i$.$e$.,$ what to buy$/$sell$/$borrow$/$lend$)$ that one should enter into to

exploit an arbitrage opportunity $($if one exists$).$ Show your work.