Towards the end of the 17th century, politicians and bureaucrats in the City of London were facing a problem not unlike the one faced by many aging cities in the early 21st century. For years, they had made promises to pay lifetime pensions to their residents, but hadn't bothered to properly estimate what those liabilities were currently worth — or how much to set aside to pay pensions. In the same vein, insurance companies were offering individual annuities to people of all ages, but were charging them a flat fixed price regardless of how old or how young they were.
In fact, various kings and queens were in the habit of borrowing money from their loyal subjects, with a promise to pay them back a lifetime pension, but had similarly never bothered to set aside or compute reserves to make those payments. According to some historians, the French treasury issued life annuities instead of regular bonds, at extremely generous yields that were the same for young and old alike. This resulted in the eventual bankruptcy of the treasury, prior to the French Revolution.
Against this backdrop, the Royal Society decided to assign this problem in early 1690 to a young and confident scientist by the name of Edmond Halley. Mr. Halley attacked this problem in a rather novel way and came up with the first formal expression for the value of a pension annuity. Yes, that is the astronomer Edmond Halley with the famous comet named after him, last seen around the solar system in 1986 and next expected to visit in the year 2061.
The astronomer Edmond Halley was a mere 35 years-old when he tackled the pricing of individual annuities, but was already widely known and respected in scientific circles around England and beyond. He wrote a famous article, which was eventually published in the year 1693 by the Royal Society in its Philosophical Transactions, where he displayed the first reliable life table. He also took the opportunity to summarize his thinking about mortality rates as a function of age, and, most importantly, laid down the foundations for determining what a pension annuity is worth.
Why a famous astronomer — who spent his time gazing at stars and comets in far-flung observatories around the world — would have been interested in working on a rather morbid problem of determining mortality rates is rather puzzling. One can speculate that his sudden interest in death might have been kindled by the fact that his father — also called Edmond Halley, a wealthy aristocrat and businessman — was alleged to have been involved in the Rye House plot. For those of you who are not English history buffs, this was a plot to kill King Charles II and his brother James in April of 1683. Anyway, to make a long story short, the king and his heir were spared and the conspirators were caught, tried and mostly executed, except for the ones who committed suicide. It's not clear if he was involved in any way, but Edmond (senior) Halley was a known associate of some of those involved and was found dead, likely murdered and completely naked except for his shoes, floating in a local river in April 1684.
Ok. I'll get back to that story and the problems this caused Edmond (junior) Halley the astronomer, later.
Take the Pension or a Lump Sum?
Nowadays, most large employers around the world — whether in the public or private sector — offer some sort of retirement savings plan to their workforce. Would you rather get a lifetime pension annuity of $1,000 per month, or a lump sum of $300,000? Are you better off taking the money out of a retirement savings plan and buying your own pension annuity? There are some tough questions people face as they near retirement, and this is precisely where Edmond Halley's pension annuity equation comes in really handy.
In sum, having an equation to figure out what a pension annuity is worth, or what it might cost to buy one, is clearly one of the most important issues that must be contemplated around retirement. For many retirees, it is the single most important decision they face. 
As you can see from the table, if you wait to purchase your pension annuity until a later age, it will be cheaper. Likewise, if interest rates move-up, your pension will become cheaper to acquire as well.
