ESIGN only applies when you want it to apply--it's totally optional and beneficial. You can ignore ESIGN until your bank wants to substitute electronic documents for the paper documents you currently use to deliver federal disclosures which are required to be "in writing."
In order to determine what applies to your e-solicitations, answer the following questions:
1. Does the content of your marketing solicitations trigger any federal disclosures?
2. If not, then ESIGN is unnecessary. If so, does the federal regulation that requires the disclosures say they must be delivered "in writing" (or similar language)?
3. If not, then ESIGN is unnecessary. If so, then what is the timing requirement for the "written" disclosures?
4. If the "written" disclosures can be provided at a later date, then compliant delivery can be accomplished using either paper or electronic documents. Otherwise, if the "written" disclosures must accompany the solicitation, then you must follow ESIGN's "informed, demonstrable consent" rules in order to obtain the customer's consent to go tree-free.
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...gone fishing.