The following is the problem that I am working on and I am having trouble.
On Jan 1 2005, an investment account is worth 100. On Apr 1 2005, the value has increased to 103 and 8 was withdrawn. On Jan 1 2007, the account is worth 103.992. Assuming a dollar weighted method for 2005 and a time weighted method for 2006, the effective annual interest rate was equal to $x$ for both 2005 and 2006. Calculate $x$.
I am puzzled because I feel as though without knowing how much the account has on Jan 1 2006, I cannot calculate either the dollar weighted or the time weighted rate of return.
If I let $A$ be the amount in Jan 1 2006, I know
$$100(1+i)+(103-8)(1+i(\frac{3}{4}))=A$$
and for 2007,
$$A(1+i)=103.922$$
I do not feel as though I am on the right track... can I have some help?
Assuming your equations are correct, you have two equations in two unknowns. If you divide the second by $1+i$, you can eliminate $A$ and have a single linear equation for $i$. The $100(1+i)$ term seems questionable because there is only one quarter to be considered there, not a full year. Your equations seem to be accounting for the interest the same way, without distinction for dollar weighted and time weighted. It seems the increase from Jan 1 2005 to Apr 1 2005 tells you the interest rate is $12\%$, making the problem overspecified.