$1.$ You are considering the possibility of participating in two investments. You estimate that the investments will yield the follow cash flows $(12$ points$)$:

Year $01234$

Investment A $-$$$100,000\mathrm{.}00$ $$21,800\mathrm{.}00$ $$47,524\mathrm{.}00$ $$38,850\mathrm{.}87$ $$14,115\mathrm{.}82$

Investment B $-$$$30,000\mathrm{.}00$ $$66,000\mathrm{.}00$ $$24,200\mathrm{.}00-$$$93,170\mathrm{.}00$ $$29,282\mathrm{.}00$

a$.$ Write a formula that defines what the IRR for each project would be $($you do not have to solve for the IRR, simply write what equation the IRR must satisfy$).$

b$.$ What is the IRR for each of the two investments? You may $($likely must$)$ use your financial calculator.