You work for Innovation Partners and are considering creating a new security. This security

would pay out $$2000$ in one year if the last digit in the closing value of the Dow Jones Industrial index in one year is an even number and zero if it is odd. The one$-$year risk$-$free interest

rate is $5\mathrm{.}3\%.$ Assume that all investors are averse to risk.

a$.$ What can you say about the price of this security if it were traded today?

b$.$ Say the security paid out $$2000$ if the last digit of the Dow is odd and zero otherwise.

Would your answer to part $($a$)$ change?

c$.$ Assume both securities $($the one that paid out on even digits and the one that paid out on

odd digits$)$ trade in the market today. Would that affect your answers?