At the beginning of January, stock $AA$ is trading at $$\frac{100}{?}$ share. Stock AAA pays a dividend of $$3$ share and is trading at $$\frac{99}{?}$ share at the end of January. A portfolio begins with $$1,000,000.$ The rate of lending and borrowing cash is $1\%$ per year.

Suppose you purchase $$500,000$ worth of AAA. What is the annualized rate of return on this portfolio in the month of January?