An investment has an installed cost of $$580,382.$ The cash flows over the four$-$year life of the investment are projected to be $$209,584,$$$253,318,$$$201,674,$ and $$169,313.$

a$.$ If the discount rate is zero, what is the NPV$?$

Note: Do not round intermediate calculations and round your answer to the nearest whole number, e$.$g$.,32.$

b$.$ If the discount rate is infinite, what is the NPV$?$

Note: A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to the nearest whole number, e$.$g$.,32.$

c$.$ At what discount rate is the NPV just equal to zero?

Note: Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$

$\backslash$table$[[$a$.$ NPV$,,],[$b$.$ NPV$,,],[$c$.$ Discount rate,,$\%$