A home in a cold climate is heated with natural gas, which costs $$8/$thousand

cubic feet, or $$1\mathrm{.}10/$therm$.$ It is estimated that raising the attic insulation level

from R$15$ to R$40$ will cost $$1200$ and save $60$ therms per year.

a$.$ Assuming a $30-$year period and a discount rate of $3\%,$ calculate the cost of

conserved energy.

b$.$ What is the simple payback period for this investment $($cost of insulation

divided by the annual savings$)?$

c$.$ Comment on why this payback is so long. Why might it still be a worthwhile

investment?