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A fund is worth $150,000 on January 1. At time t (0 < t < 7/12) the fund value has increased to $156,000. A deposit

A fund is worth $150,000 on January 1. At time t (0 < t < 7/12) the fund value has increased to $156,000. A deposit of $20,000 is then made. On August 1, the fund value is $180,000. A withdrawal of $25,000 then made. On December 31 the value of the fund is $160,000. The dollar-weighted return is equal to the time-weighted return. What is t?

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