Interest is not usually paid on escrow accounts operated by independent escrow agents because the compliance overheads and ongoing costs are generally very high and many safeguarding/segregated account facilities come at a high cost.
Most escrow agents (including us) will, instead, apply any interest towards the fee for the service in order to keep the fees down - in this way, the third-party bank contributes to the fees, rather than one of the parties.
Private escrow accounts provide security, trust and transparency to ongoing or ad-hoc payment requirements.
Third-Party Managed Accounts (TPMA's) are a convenient way to manage complex, high-value or even routine payment operations.