Light emitting diode $($LEDs$)$ light bulbs have become required in recent years, but do they make financial sense? Suppose a typical $60-$

watt incandescent light bulb costs $$\mathrm{.}55$ and lasts for $1,000$ hours. A $15-$watt LED, which provides the same light, costs $$3\mathrm{.}90$ and lasts

for $12,000$ hours. A kilowatt hour of electricity costs $$\mathrm{.}131.$ A kilowatt$-$hour is $1,000$ watts for $1$ hour. However, electricity costs actually

vary quite a bit depending on location and user type. An industrial user in West Virginia might pay $$\mathrm{.}04$ per kilowatt$-$hour whereas a

residential user in Hawaii might pay $$\mathrm{.}25.$ You require a return of $11$ percent and use a light fixture $500$ hours per year. What is the

break$-$even cost per kilowatt$-$hour?

Note: Do not round intermediate calculations and round your answer to $6$ decimal places, e$.$g$.,32\mathrm{.}161616.$