A firm invests $$1,000,000$ in its short$-$term investment portfolio at the beginning of the year. It deposited $$250,000$ and $$145,000$ at the end of the first and second quarters, respectively. A withdrawal of $$450,000$ was made from the short$-$term investment portfolio at the end of the third quarter. At the end of the fourth quarter, the short$-$term investment portfolio had a market value of $$1,300,000.$ Based on this information

a$.$ Calculate the money$-$weighted rate of return earned on the portfolio.

b$.$ Annualize the value from part A using the APR and EAR approaches.