Given the cash flows below, answer the following question $($provide your answer and show your work in your uploaded document$)($maximum points: $3\mathrm{.}33)$

$\backslash$table$[[$Date$,$Cash Flow,Balance$],[\frac{7}{1},$Begin,$2,150],[\frac{7}{31},--$cdots,$2,280],[\frac{8}{1},$$$180,2,460],[\frac{8}{31},----,2,561],[\frac{9}{1},$$$100,2,661],[\frac{9}{30},$End,$2,500]]$

Calculate the average monthly rate of return using the money $($dollar$)$weighted method over the three months provided here $($round your answer to $3$ decimals in the form $0\mathrm{.}000)$ Show your work in the uploaded document: