An investment fund accumulates with force of interest t = K 1+(1t)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.