Please do not use the excel function.

Qin Jiushao deposits 1,000 into a fund on January 1, 2020 and then another deposit of unknown amount into the fund on July 1, 2020. On January 1, 2021, the balance in the fund is 2,000. Noting that the time-weighted yield rate is 10% and the dollar-weighted yield rate is 9%, calculate the annual effective interest rate earned on the fund during the first six months of 2020