$($Related to Checkpoint $5\mathrm{.}6)($Solving for $i)$ You are considering investing in a security that will pay you $$3,000$ in $26$ years.

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

b$.$ Assume these investments sell for $$1,152$ in return for which you receive $$3,000$ in $26$ years. What is the rate of return investors earn on this investment if they buy it for $$1,152?$

a$.$ If the appropriate discount rate is $11$ percent, the present value of this investment is $$198\mathrm{.}94.($Round to the nearest cent.$)$

b$.$ The rate of return investors can earn on this investment if they buy it for $$1,152$ is $\%.($Round to two decimal places.$)$