You are presented with an investment opportunity that will give you the following stream of cash flows: nothing for the next $2$ years; starting at the following year, an amount of $$4,000$ per year until year $10$; and after that year, an amount of $$8,000$ per year until year $21.$ If your required rate of return $($APR$)$ is $11\%$ compounded annually, what is the present value today of these cash flows?