Русско-англо-русский юридический словарь

Because immediately seems to promise more than it can deliver, you should omit it from your contracts for purposes of obligations and conditions. Use promptly instead. If you want a standard more demanding than promptly, specify a limit in days. Or combine the two standards—promptly, but in no event later than X days after …. One exception is where you’re seeking to express a real sense of urgency, as in If Service Provider detects any unauthorized use of a User’s account, Service Provider shall suspend that account immediately. (Adams on Contract Drafting)

The net effect is that for purposes of contract drafting, promptly and immediately mean the same thing. (Obviously, the same goes for expeditiously, as soon as practicable, forthwith, and the like, as well as the adjectives prompt and immediate.) I hear you saying, How can this be? Here’s my take on it: In idiomatic usage, immediately can mean “instantly”—I didn’t hear what John said, but Mathilde immediately turned and walked away. By contrast, promptly conveys a sense that some time would be required. Promptly can be used to mean “instantly,” but only if you’re aiming for a slightly droll effect—I didn’t hear what John said, but Mathilde promptly turned and walked away. (Adams on Contract Drafting)

‘we undertake to pay forthwith the money required’ (Oxford English Dictionary)