Give typed solution with good explanation

On January 1, an investment account is worth 50,000. On June 1, the value has increased to 52,000 and 8,000 of new principal is deposited. At time t, in years, (4/12 < t < 1) the value of the fund has increased to 62,000 and 10,000 is withdrawn. On January 1 of the next year, the investment account is worth 55,000. The dollar-weighted rate of return (using the simple interest approximation) is equal to the time-weighted rate of return for the year.

Calculate t.

(A) 0.7411 (B) 0.7415 (C) 0.7585 (D) 0.7589 (E) 0.7885