The current lease allows the company to sublease the facility, so they have decided to sublease the facility to another company for $$50,000$ each year $($$$10,000$ less than the current lease payment$).$

They have found $4$ possible facilities that will meet their needs. Each is similar, so the only difference that the company is considering is the price that they will pay to lease the facility for the next $10$ years. The following are the prices:

$1.$ Pay a single fee at the beginning of the lease of $$833,300$ and receive $$100,000$ back at the end of the $10-$year lease term.

$2.$ Pay $$51,250$ Semiannually with the first payment due at the end of the first $6$ months.

$3.$ Pay $$25,550$ Quarterly with the first payment due at the time the lease is signed$/$the term begins.

$4.$ Pay $$8,600$ Monthly with the first payment due at the time the lease is signed$/$the term begins.

$*($They have a $5\mathrm{.}75\%$ annual return rate on investments. Use this rate for all needed calculations.$)$

$**($If there is a payment, the compounding of interest and payments occur at the same time.$)$

The COO has asked you to determine how they should account for the first lease as of the cease$-$use date and to determine which of the $4$ buildings is the best option for the new lease.