$($Related to Checkpoint $5\mathrm{.}6)($Solving for i$)$ You are considering investing in a security that will pay you $$2,000$ in $29$ years.

a$.$ If the appropriate discount rate is $9$ percent, what is the present value of this investment?

b$.$ Assume these investments sell for $$378$ in return for which you receive $$2,000$ in $2$ years. What is the rate of return investors earn on this investment if they buy it for $$378?$

a$.$ If the appropriate discount rate is $9$ percent, the present value of this investment is $ $.($Round to the nearest cent.$)$