a pension fund began a year with a balance of $$1,000,000.$ there were contributions to the fund of $$200,000$ at the end of february and again at the end of august. there was a benefit of $$500,000$ paid out of the fund at the end of october. The balance remaining in the fund at the start of the next year was $$1,100,000.$ Find the dollar$-$ weighted annual rate of return earned by the fund