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

security would pay out $$1000$ 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 $5\%.$ Assume that all investors are averse to risk.

a$)$ What would be the risk$-$premium on this security? Its expected return?

b$)$ What would the security$$s price be$?$