$($Related to Checkpoint $5\mathrm{.}6)($Solving for $i)$ You are considering investing in a security that will pay you $$3,000$ 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 $$1,646$ in return for which you receive $$3,000$ in $30$ years. What is the rate of return investors earn on this investment if they buy it $$1,646?$

a$.$ If the appropriate discount rate is $11$ percent, the present value of this investment is $$.($Round to the nearest cent.$)$