On January 1, an investment account is worth 50,000. On May 1, the value has increased to 52,000 and 8,000 of new principal is deposited. At time t, in years, (4/12

The question is incomplete. The complete question is :

On January 1, an investment account is worth 50,000. On May 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 1) the value of the fund has increased to 62,000 and 10,000 is withdrawn.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 approximate dollar-weighted rate of return (using the simple interest approximation) is equal to the time-weighted rate of return for the year. Calculate t.

Solution :

It is given that :

Worth of investment account on 1st Jan = 50,000

Worth of investment account on 1st Jan next year = 55,000

New principal deposited = 8000

Therefore the interest earned = 55,000 - 50,000 - 8,000 + 10,000

                                                  = 7,000

Therefore,

                   = 0.13667

7000 = 0.13667(55,333.33 - 10000 + 10000t)

    = 0.5885

Thus, time - weighted rate of the return = 0.5885