Natalie Davis is at home barricading the doors and windows, and then glances nervously at her grandfather clock. It shows a half-hour before midnight and Natalie calls her sister-in-law Virginia and asks if Natalie's husband Michael is there. Virginia says that he hasn't been back since Natalie called a half hour ago and Natalie begs her to tell Michael that she's sorry and to come back to her. Virginia says that she'll give her brother the message and asks if there's anything that she can do, and Natalie says that she isn't and then hangs up.
The phone rings a minute later. It's Michael, who tells Natalie that he's staying at a hotel room and will be back in the morning to get his things and move out for good. Natalie begs him to come over and rambles about a Mr. Tickton and how he will take her away. Michael has no idea what Natalie is talking about and tells his wife to start from the beginning.
Two weeks ago, Natalie comes out in the morning and finds Michael in the kitchen feeding their dog, Tina. He insists that he'll be to work on time but Natalie tells him to get going, worried that he'll arrive late. The mailman drops off the mail and Michael finds a letter to Natalie among the bills. It's an invitation to her from a new bank in town, asking her to come by and sign up to become a depositor. They figure that it's a joke since they don't have that much money, and Natalie tells Michael that she'll visit them later and explain that they're not interested. As Michael leaves for work, Natalie tells him to fix the leg on her grandfather clock when he gets home. He says that he'll get around to it eventually and complains that she's always pressuring him to keep to a schedule. Natalie insists that a schedule is important and watches as he leaves.
That afternoon, local handyman Ed Harris arrives at the bank and the president, Tickton, asks if he has more to deposit. Harris assures him that he does and that he's saving even more time by finding a shortcut to work. The bank president thanks him for his hard work just as Natalie arrives. She glances at the walls, which are covered in clocks, and tells Tickton that he must have made a mistake inviting her to become a member. Tickton tells her that the reports they have on her are very good and invites Natalie to sit down. When she asks about the strange clocks and the lack of guards, Tickton explains that they don't store money... they store time.
When Natalie wonders what he means, Tickton admits that he and his people are aliens and that they have set up a banking franchise on Earth. Their depositors record and donate all of the time that they have saved and then store it at the bank. Tickton and his people can transfer the time to their homeworld, tabulate it, and let it collect interest. Natalie doesn't see the point and Tickton explains that she can use the time they return to her and the interest to extend her own life.
Harris finishes his deposit and greets Natalie, who recognizes him. he assures her that the time bank is the best thing that ever happened to him and that he has already saved 36 hours in the month since he signed up. Once he leaves, Tickton explains that she records her time savings in a deposit book, and shows her a ledger of famous people that are depositors with the bank. Impressed, Natalie wants to talk to her husband but Tickton warns her that because of their alien nature, she can't discuss it with anyone. Michael, who likes to waste time, doesn't qualify as a depositor. Natalie finally signs the bank contract and Tickton congratulates her on joining the bank.
At ten minutes to midnight, Natalie finishes the first part of her story. Michael insists that it makes no sense and Natalie tells him that Tickton is coming for her. He wonders why and Natalie explains that she accumulated enough saved time to deposit twelve hours, but then everything went wrong.
That Sunday, Michael is trying to relax with the newspaper but Natalie hounds him into working on the house and fixing the grandfather clock. She complains that he's wasting time and Michael points out that in the last two weeks she has become even more obsessed with time. He asks her about the new deposit book she has been hoarding over but Natalie refuses to discuss it. Michael agrees to start on the work once he feeds Tina, and Natalie reluctantly tells him that she got rid of the dog. She insists that it was old and would have died anyway, so she gave it to the pound. Furious, Michael says that he's had enough and that once he gets Tina, he'll be moving out. Natalie begs him to stay, saying that she'll get Ed Harris to do the work, and Michael tells her that Harris died the previous day. Natalie is surprised since the fact Harris was a depositor should have given him more life, not less.
Michael leaves before Natalie can stop him. When she runs to the door, she finds Tickton there. Natalie wonders why he's there on a Sunday and Tickton explains that there has been a crisis on their planet. They need the extra time more than ever, so they are exercising a clause in the depositor contracts to collect all of their time immediately. Tickton can only give her until midnight that night to put her affairs in order, and after that he has to collect all of her time. Natalie screams at him to get out and Tickton leaves, pausing only long enough to admire the accuracy of her grandfather clock.
At three minutes to midnight, Natalie finishes her story and begs Michael to come home. Before he can respond, the line goes dead. When Natalie tries to call her husband back, she gets a telephone clock telling her the time is 11:59. Tickton arrives at the door and rings the bell, telling Natalie that she should be considerate and come with him. Natalie finishes barricading the door and the backs up against the grandfather clock. It starts to chime midnight... and then the leg breaks off and it falls on her, crushing her to death.