You are considering investing in a security that will pay you $$1,000$ in $25$ years.

a$.$If the appropriate discount rate is $8$ percent, what is the present value of this investment?

b$.$Assume these investments sell for $$565$ in return for which you receive $$1,000$ in $25$ years. What is the rate of return investors earn on this investment if they buy it for $$565?$