$($Related to Checkpoint $5\mathrm{.}6)($Solving for i$)$ You are considering investing in a security that will pay you $$1,000$ in $26$ years.

a$.$ If the appropriate discount rate is $10$ percent, what is the present value of this investment?

b$.$ Assume these investments sell for $$238$ in return for which you receive $$1,000$ in $26$ years. What is the rate of return investors earn on this investment if they buy it for $$238?$

a$.$ If the appropriate discount rate is $10$ percent, the present value of this investment is $$83\mathrm{.}91.($Round to the nearest cent.$)$

b$.$ The rate of return investors can earn on this investment if they buy it for $$238$ is

$\%.($Round to two decimal places.$)$