On January 1, a fund is worth 100,000. On May 1, the value has increased to 120,000 and then 50,000 of new principal is deposited. On November 1, the value has declined to 130,000 and then 30,000 is withdrawn. On January 1 of the following year, the fund is worth 120,000. Determine the time-weighted rate of return. You may assume that each month contains an equal number of days