$13.$ QuantumSoft Solutions is considering expanding its AI research department, which will also

involve a significant investment in cloud computing infrastructure. QuantumSoft requires an

$8\%$ return per year for the project. The project is expected to generate additional revenue

of $$500,000$ annually for the next three years and $$1,500,000$ annually for the following five

years. What is the maximum initial expense that QuantumSoft should be willing to make for

the investment?

$($a$)$ $$8,425,067$

$($b$)$ $$2,892,324$

$($c$)$ $$10,555,178$

$($d$)$ $$1,100,543$

$($e$)$ $$6,042,861$