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An investment fund accumulates with force of interest dt = K 1+(1-t)K for 0 = t = 1. At time zero, there is $100,000 in the fund. At time one, there is $110,000 in the fund.

The only two transactions during the year are a deposit of $15,000 at time 0.25 and a withdrawal of $20,000 at time 0.75. Calculate K.

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