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"Science fiction has gotten more accurate as we've gotten closer to the present, because science fiction stories have not only attracted, but also generated current scientists."
- Larry Niven

Universal Checkbook  
  Fully electronic banking system, which allows easy withdrawal of funds from any bank.  

Heinlein wasn't the first person to think of applying computers to banking. In fact, researchers at the Stanford Research Institute invented "ERMA", the Electronic Recording Method of Accounting computer processing system in the mid-1950's. ERMA computerized the manual processing of checks and account management and automatically updated and posted checking accounts. Stanford Research Institute also invented magnetic ink character recognition as part of ERMA.

ERMA was first demonstrated to the public in September of 1955, and was first used on real customer accounts in the fall of 1956. General Electric delivered thirty-two units to the Bank of America in 1959 for full-time use as the bank's accounting computer and check handling system. ERMA computers were used well into the 1970s.

Even so, getting money from a bank not your own was still a problem, since you had to wait for the check to clear (you still do!). Heinlein's system has the advantage that all of the banks are connected by the same network, allowing any bank to hand out your money. And that didn't happen until the mid-1980's.

I could have saved time by hiring a cab to jump me to Riverside, but I was handicapped by lack of cash. I was living in West Hollywood; the nearest twenty-four-hour bank was downtown at the Grand Circle of the Ways. So first I rode the Ways downtown and went to the bank for cash. One real improvement I had not appreciated up to then was the universal checkbook system; with a single cybernet as clearinghouse for the whole city and radioactive coding on my checkbook, I got cash laid in my palm as quickly there as I could have gotten it at my home bank across from Hired Girl, Inc.
From The Door Into Summer, by Robert Heinlein.
Published by Unknown in 1956
Additional resources -

By the way, the next step in the banking chain, the Automatic Teller Machine, was introduced to customers in 1969. Don Wetzel holds the patent with two other men; appropriately, he thought of the ATM while waiting in line at a Dallas bank. At the time (1968) he was the Vice President of Product Planning at Docutel, a company that developed automated baggage-handling equipment.

(Thanks to Joel Terrill for suggesting this one.)

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Additional resources:
  More Ideas and Technology from The Door Into Summer
  More Ideas and Technology by Robert Heinlein
  Tech news articles related to The Door Into Summer
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