How is cost of soldiers calculated?

I had 18 soldiers in three different locations at a training cost of 600 something. I decided I could not afford that for the moment so I sacked 12 soldiers. To my surprise I still have almost 600 in training cost for soldiers. Why did I not get 1/3 of the cost when I reduced the no of soldiers? Or is it the military buildings that costs a lot? (I have four of them but currently only soldiers in two of them)

It’s the buildings, not the number of soldiers iirc. Same for the defense towers.

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I removed one of the four barracks and to my surprice the cost for the sodiers went up (!) (601 vs 585). Wonder how that happened?

Looking at the Game Guide:

“Once a Barracks is constructed, you can assign villagers to be soldiers. This has an upfront gold cost, and then each soldier has an additional upkeep for training and compensation.”

Doing a search I can see some replies from Zantai about halting production on defense towers to cut their costs; don’t know if the same is possible for barracks.

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Yes, you can halt production of soldiers at towers and barracks. Then you stop to pay for soldiers for as long as the production of the building is stoppped. And you have to do that for every tower and barracks you want.
Actually it is possible to halt production for every single building if i’m correct.