On January 1, an investment account is worth $100,000. On May 1, the account value has increased to $112,000, and $30,000 of new principal is deposited. On November 1, the account value has decreased to $125,000, and $42,000 is withdrawn. On January 1 of the following year, the account value is $100,000. Compute the yield rate using

(a) the dollar-weighted method and

(b) the time-weighted method.

Please show all formulas and work, do not use excel!