Concept

• If we make contributions and withdrawals at time points that are within one time interval, we can weight those dollar intervals to get the final balance in the account at the end of the time period

Solution

Dollar-Weighted RoR

• It’s just doing accumulated values but with negatives for account contributions
• Basically, it’s just the IRR

If given a table, it would be (for a linear approximation):

Time-Weighted RoR

• The product of all the individual interests equals $(1+i)$
• To find the $j$‘th interest from a table of balances and contributions: $$\frac{B_{t_{k}}}{B_{t_{k-1}}+C_{{t_{k-1}}}} -1$$