Benjamin Franklin Left Two Cities Money in 1790. They Got It in 1991.
In 1991, officials in Boston and Philadelphia sat down to account for something peculiar: two trust funds that had been sitting largely untouched for two hundred years. Benjamin Franklin had set them up in his will in 1790, leaving 1,000 pounds sterling to each city. The interest had been accruing since before the American Constitution was one year old. The number they arrived at was around 20 million dollars each.
Franklin had calculated this in advance. He wrote in his will that after one hundred years, each city could withdraw a portion for public works, and the remainder should keep compounding for another century. His projection for the two-hundred-year mark was approximately four million pounds per city. He was off by a factor of five. The money grew more than he expected because reinvested interest generates its own interest, recursively, in a way that human intuition consistently underestimates.
The Mathematics Franklin Understood
Franklin understood compound growth better than most people of his era. He had spent enough time as a printer and then as a businessman, postmaster, and diplomat to understand how small, regular surpluses accumulate over time. The formula itself had been known since the Italian Renaissance, when bankers in Florence and Genoa applied it to loans. But knowing the formula and understanding its long-run implications are different things. His own observation was direct: Money makes money. And the money that money makes, makes money. That sentence sounds obvious. The mathematics behind it is not.
When you deposit a principal sum at any rate of interest, the first year's growth is simple to follow. One thousand dollars at five percent earns fifty dollars. The difficulty begins in year two, when the calculation applies the same rate not to the original thousand but to the thousand and fifty. The next year, the base grows again. And again. Each cycle, the base is slightly larger, so the absolute dollar amount added is slightly larger, so the next cycle adds still more. The curve is not linear; it accelerates. After a decade, the fifty-dollars-a-year figure has become something closer to eighty. After two decades it has roughly tripled. After a century, the original thousand dollars has become one hundred and thirty thousand under Franklin's projected five percent rate.
The concept was not even original to Franklin. A French satirist named Charles-Joseph Mathon de la Cour had written a parody of Franklin in 1785, in which a fictional philanthropist bequeathed a small sum to be invested for five hundred years before anyone could touch it. Franklin read the parody and liked the underlying premise enough to use it, adjusting the timeline to something more practically verifiable.
How the Two Cities Diverged
What is interesting about the Boston and Philadelphia experiment is that the two cities did not end up with the same amount despite starting with identical sums. Philadelphia followed Franklin's original intent: it loaned money to young tradespeople at modest rates to help them start businesses, collecting repayments, relending the capital, letting the proceeds from those loans compound into further loans. Boston took a different approach, investing more conservatively through a trust structure oriented toward preservation. By 1991, the different compounding rates produced noticeably different outcomes. Boston had roughly 4.5 million; Philadelphia around 2 million. The divergence is a concrete demonstration that the rate compounds as dramatically as the time.
This is why compound interest calculations make the nonlinearity visible. You can input the same scenario three times with different rates, say three percent, five percent, and seven percent, and watch the outcomes separate dramatically over thirty years. The three percent scenario does not produce half the result of the six percent scenario. Because of compounding, it produces something like one quarter. The gap is not proportional to the rate difference. It widens exponentially.
This is the thing that compound interest calculations make visible: the nonlinearity. Each period's larger interest payment becomes part of the next period's earning base. The effect multiplies itself. Over long timescales, small rate differences produce outcomes that are not proportional but exponential.
The 200-Year Demonstration in Practice
Franklin's bequest was, among other things, a demonstration aimed at posterity. He knew he would be dead before the point was made. He set up the experiment precisely because it could not be argued with. You cannot debate a trust fund that has been running for two hundred years. The math was not a theory by 1991. It was an account balance.
Two hundred years is obviously not the timescale most people are working with. But the mathematics scales down proportionally. The same exponential curve that turned 1,000 pounds into 20 million dollars over two centuries describes what happens to a retirement account over forty years, a college savings fund over eighteen, or a side investment over a decade. The curve does not require 200 years to be meaningful. It requires only patience and a rate.
Conclusion
The way to understand your own numbers is to put them in a calculator and let the math run. Change the rate by two percent and look at what happens to year thirty. Change the starting amount and watch how the curve shifts. Franklin made his point with a will and a two-century wait. You can arrive at the same understanding in about ninety seconds.
ToolHQ's compound interest calculator lets you model any principal, rate, and time horizon. Change one variable and watch the output recalculate immediately. You can compare scenarios side by side: the same starting amount at different rates, or different starting amounts at the same rate, laid out over your actual time horizon rather than a hypothetical two centuries.
Frequently Asked Questions
What did Benjamin Franklin's compound interest experiment actually prove?
That 1,000 pounds invested at modest rates in 1790 would become roughly 20 million dollars by 1991. The experiment demonstrated compound growth's nonlinearity in a form that couldn't be argued with: a real account balance.
Why did Boston and Philadelphia end up with different amounts from identical starting gifts?
Different investment strategies produced different effective compounding rates. Philadelphia loaned money to tradespeople and relent repayments; Boston invested more conservatively. Small rate differences compound dramatically over 200 years.
What is the difference between simple and compound interest?
Simple interest applies only to the original principal. Compound interest applies to the principal plus all previously earned interest, so the earning base grows every period and the curve accelerates over time.
Why does doubling the interest rate more than double the outcome?
Because each period's larger interest payment becomes part of the next period's earning base. The effect multiplies itself. Over long timescales, small rate differences produce outcomes that are not proportional but exponential.