You are considering investing in a security that will pay you $$$$1,000$ in $30$ years.

a$.$If the appropriate discount rate is $11$ percent$,$ what is the present value of this$$ investment?

b$.$Assume these investments sell for $$$$498$ in return for which you receive $$$$1,000$ in $30$ years. What is the rate of return investors earn on this investment if they buy it for $$$$498?$