Peterson Packaging Incorporated does not currently pay dividends. The company will start with a $$0\mathrm{.}50$ dividend at the end of year three and grow it by $10\%$ for each of the next six years until it nearly reaches $$1\mathrm{.}00.$ After six years of growth, it will fix its dividend at $$1\mathrm{.}00$ forever. If you want a $15\%$ return on this stock, what should you pay today, given this future dividend stream? Please show your work