Full problem:
Arthur buys $\mathbb{$}2000$ worth of stock. Six months later, the value of the stock has risen to $\mathbb{$}2200$ and Arthur buys another $\mathbb{$}1000$ worth of stock. After another eight months, Arthur's holdings are worth $\mathbb{$}2700$ and he sells off $\mathbb{$}800$ of them. Ten months later, Arthur ands that his stock has a value of $\mathbb{$}2100$.
(a).Compute the annual time-weighted yield rate of the stock over the two-year period. (b).Compute the annual dollar-weighted yield for Arthur over the two-year period.
I calculated (a) very quickly (it is $1.289\%$). The problem I've been having is calculating the annual dollar-weighted yield. I calculated a value of of $4.24\%$, but apparently the answer is $-2.09097\%$. My attempt was as such:
Let $s$ denote our dollar-weighted yield rate. We use simple interest, so
$$2100=2000(1+2s)+1200(1+\frac{18}{12}s)-1300(1+\frac{10}{12})$$ $$\implies 200=4716.666667s$$ $$\implies s=4.24\% \neq -2.09097\%$$
So can anyone give me a hand? From my results, I've come to the conclusion that I don't know what I'm doing with dollar-weighted yield
I would calculate $2000*(1+x)^2+1000*(1+x)^{18/12}-800*(1+x)^{10/12}=2100$
The result is $-2.09097\text{%}$.