The simplico gold mine has a great deal of remaining gold

deposits, and you are part of a team that is considering leasing

the mine from its owners for a period of $10$ years. Gold can be

extracted from this mine at a rate of up to $10,000$ ounces per

year at a cost of $$200$ per ounce. This cost is the total

operating cost of mining and refining, exclusive of the cost of

the lease Currently the market price of gold is $$400$ per ounce.

The interest rate is $10\%.$ Assuming that the price of gold, the

operating cost, and the interest rate remain constant over the

$10$ years period, what is the present value of the lease?