Short answer: Don't do it. It's expensive. A 410 gold item will cost over $300.
Long answer: A discussion came up last night involving the notion of dumping some cash into purchasing precursors. Precursors tend to be expensive, depending on which one is needed, and so any alternative means of gaining access to one seems to be more cost effective than spending the time to save up in-game money.
Of course, not all alternatives are created equal, and I would recommend against going the raw cash route unless you happen to fancy spending several hundred dollars on a set of pixels. I know that seems a bit absurd (and it certainly is), but precursors are surprisingly cost prohibitive.
The reason we come to this conclusion is because gold in Guild Wars 2 is delightfully tied to something we can measure. Specifically, we can measure the fluctuating cost of converting gems (earned by cash) into game currency. So, although this means there is an intermediary between converting real world money into gold (via the gems), this isn't any different than dealing with a real world currency exchange rate. The strength of a gem's purchasing power therefore dictates how much gold you'll receive. Sadly, as the market currently stands right now, the purchasing power of a single gem is very poor. ArenaNet isn't liable to complain, either. You'll see why in a moment.
First, I'm not the smartest block in the knife drawer, so I like to use easy to process numbers.
Gems currently run for 1600 per $20. Breaking this down to a "per dollar" rate yields 80 gems per dollar. According to the current currency exchange rate, 100 gems will net you 1g50s20c. Since 80 gems is conveniently 80% of 100 gems, that means that a single dollar will purchase about 1g20s16c. That sadly isn't very much. Extrapolating to find the amount of dollars we'd need to purchase a 410 gold item then yields about (1.2016x = 410, solving for x = math.ceil(410 / 1.2016)) $341.22. The plus side is that the dollar is currently stronger than the GW2 gold, which may not be representative of the current real world economy.
Interestingly, the exchange rate doesn't quite work backwards due to what I can only surmise is a trading post "tax" of about 26.846%. If you were to attempt to purchase 100 gems, you'd need to fork over about 2g5s32c at the current rates as of this writing. It'd be interesting to see if this tax is relatively consistent or not as the prices fluctuate.
Edit: The curious thing about this thought experiment is, taken to its logical extreme, netting some 5 gold after several hours worth of dungeon runs implies we're working for far less than minimum wage.