I was looking at this question and I think I may have read the same story, but I'm not sure because a few of the details don't quite line up.
The story I read was about a man who had built a machine that could work out when a person would die. The way it worked was described as sending a small electric charge along the four-dimensional "sausage" which was a person's extent in spacetime - the story definitely used the word "sausage". The person who had built the machine had made several predictions which he put in sealed envelopes, including that of his own death. The story ended with him being visited by a pregnant woman who wanted to know how long her child would live. The builder saw that she would die very soon, and tried to keep her in his office as long as possible to avoid her fate by giving her tea and cakes, but she insisted on leaving and got hit by a car as she crossed the road to leave his office. This caused him to kill himself, and the date in his envelope was correct.
I read this in 1999 at the earliest and 2001 at the latest. Around the same time - possibly but not definitely in the same book - I read a story about a murder mystery in which the murder weapon turned out to be a time-accelerated flashlight.
I tried googling with these details, but kept running into the Machine of Death anthology which made it very difficult to find earlier stories on that theme.
Answer
That is "Life-Line" by Robert Heinlein.
You pretty much nailed the story.
Only, Pinero (the man with the machine) didn't kill himself. He was killed by a contract killer who was paid by the head of an insurance company.
Pinero was advising people on how long to plan their lives. Insurance companies sued him because they were losing money on people who knew when they were going to die.
In court, he was challenged to prove he could really predict the life span of people. He measured the life span several lawyers and the heads of the companies. They then met periodically to open the sealed predictions.
Pinero, of course, had measured the length of his own life and knew when he was going to die. He had a last meal and a favorite liqueur shortly before the killer arrived.
The final scene has the heads of the insurance companies meeting again. Pinero is dead, and his date is in the current envelopes to be opened. The heads of the companies collect all the sealed prediction envelopes and burn them in a trash can right there in the meeting room.
The story is later linked into the Lazarus Long stories. The woman turns out to have been Lazarus' mother, whom he rescues with the help of a time travelling spaceship. He plucks her out of place just as the accident occurs. This is several hundreds (if not thousands) of years later in Lazarus' time line.
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