$($a$)$ Give the meaning of each of the following terms:

$($i$)$ Effective Annual Interest Rate $($EAR$)$

$($ii$)$ Stated Annual Interest Rate

$($iii$)$ Annuity

$($iv$)$ Perpetuity

$($b$)$ A company's assets grew from $$1537205$ in $2015$ to $$3213841$ in $2021.$ Calculate the average annual growth rate of the company's assets.

$($c$)($i$)$ Define Net Present Value $($NPV$)$ and state the NPV rule.

$($ii$)$ Define Internal Rate of Return $($IRR$)$ and state the IRR rule.

$($d$)($i$)$ You are looking at investing $$1800000.$ This investment will generate $$400000$ at the end of year $1,$$$450000$ at the end of year $2,$ and $$600000$ at the end of year $3.$ Using $7\mathrm{.}5\%$ as the discount rate, calculate the NPV$.$ Should you accept this investment? Why or why not?

$($ii$)$ Determine the IRR for an initial outlay of $$3\mathrm{.}5$ million, and a cash flow of $$275000$ per year into perpetuity.