Sometimes, a money bag will spawn in a less than ideal spot for growing conditions. For a tree to reach maturity, it needs each 1x1 space around it to be free, meaning you can't have any objects like rocks or flowers adjacent to it, and it can't be right next to the water. Also, if you have any sort of pavement or custom design ground covering adjacent to your tree, it will not grow. If you have a dirt path alongside it, however, it will still grow.
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The good news is, once you have established your money tree sapling, you can transplant it wherever you would like it to grow on your island. Some players establish a money tree grove where money trees in various stages of maturity all grow in one spot. Once one bears "fruit," you can shake it, chop it down, remove the stump, and plant your new sapling in the hole that remains.