FBO is a industry-wide, accepted term by all IRA custodians. It helps maintain the administration chain for an IRA along with the asset ownership: the person for who's benefit the custodian holds the money.
FBO is used in self-directed, inherited, education and transfer IRA structures. The custodian will always be listed first, with the person who is entitled to the assets designated after FBO.
When trustee-to-trustee transfers are made, the checks issued are made payable to your new trustee FBO. This is unlike a rollover, where you are able cash the check because it is made payable to you.
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The significance of the FBO designation lies with the IRS. Money movements and transfers made through an FBO do not generate a 1099-R and therefore don't generate taxes.
Do not confuse all FBO designations as IRA accounts. An FBO may be utilized in a trust or charitable contribution designation as well.