A company purchase a piece of manufacturing equipment for an additional income. The expected income is $$4,500$ per semester. Its useful life is $9$ years. Expense to be $$500$ semiannually. If the purchase price is $$45,000$ and there is a salvage value of $$4,500,$ what is the prospective rate of return $($IRR$)$ of this investment? The compounded semiannually.

a$.$ IRR $=6\mathrm{.}02\%$ semiannual

b$.$ IRR $=12\%$ semiannual

c$.$ IRR $=396$ semiannual

d$.$ IRR$=6\mathrm{.}23\%$ semiannual