On January 1st, an investment is worth $100. On April 19th, the value is $95 and $2X is deposited right afterwards. On October 30th, the value is $105 and $X is deposited right afterwards. On January 1st of the following year, the investment is worth $115. The dollar-weighted rate of interest for this one-year period is 0%. Calculate the time-weighted rate of interest.