Composite Longbow crafting question

[ArtenDaelus]

So i want to boost my composite longbow str rating from +1 to +3
My question is do i only need 67 gold or do i need 134 gold to craft a composite longbow +3.
And how much time per day do i spend on crafting?

[Coventry]

A non-masterwork composite Longbow rated for Strength 12 (+1) has a standard cost of 200 gp.
A non-masterwork composite Longbow rated for Strength 16 (+3) has a standard cost of 400 gp. Reference: d20pfsrd (https://www.d20pfsrd.com/equipment/weapons#martial-ranged)

The rules for crafting mundane items are here (https://www.d20pfsrd.com/skills/craft/).

That section of rules talks about upgrading a normal item to a masterwork by simply taking the base item and paying for the masterwork component, so the precedent is that you can upgrade the bow by covering the difference in the two costs (200 gp). The raw materials needed to make the change is one third to start, so 66.67 gold. It could be more, if you roll poorly.

Here's the first catch: the crafting DC for a Composite Bow is 15+2xrating, or 21 in this case. If your d20 crafting check for a week is 16 or lower, you lose half the raw materials and have to replace them to continue. Every failed die roll increases the cost by another 33.33 gold. Fail four times before completing the upgrade, and your total raw materials cost has hit the full 200 gold. Fail 10 times, and you've spent as much as if you had simply bought the new bow at full retail.

Fortunately, crafting does not fail on a d20 roll of natural 1, so you can get rid of the risk of loss if your bonus for crafting checks is +16 or higher.

Here's the second catch: your progress towards completion for a week's worth of effort is only the product of the die roll and the Crafting DC, and is compared against the total cost of the upgrade in silver pieces (2000 in this case). Assuming you get the +16 bonus, you make no progress on a die roll of 1-4, and otherwise make progress at an average of (28.5 x 21 )= 598.5 silver pieces for a week's worth of work. It takes 4 weeks of successful crafting checks to exceed 2000 silver. You will likely have one week where you don't make progress.

Five weeks. It's a full time job with no time for adventuring. Ouch.

It is not easy for a first level character to reach a +16 crafting bonus, but it is possible without spending feats (1 rank, +3 class skill, +5 INT, +2 masterwork artisan tools, +5 luck from casting Crafter's Fortune).

A 20th level character can hit a crafting bonus of +50 or higher, and can use the accelerated crafting rules to increase the DC to 31 ... and still only averages about 1,875 silver pieces of progress in a full week's worth of work. That is not enough, so it still take that character two weeks to improve that bow.

Seems ludicrous, doesn't it? Magic Item crafting proceeds at a rate of up to 1000 gp per day.