Ben Franklin's Will - Web Reading for Lab
This all actually happened! It is a great project since it combines financial mathematics with the disciplines of history, economics, political science, ethics and philosophy. In addition, it gives you a chance to see how interest is actually earned by a fund or a bank when they loan out money. Read the following in preparation for lab.
Ben Franklin's plans

In 1785 a French mathematician named Charles-Joseph Mathon de la Cour wrote a parody mocking the spirit of American optimism represented by Franklin. The Frenchman wrote a piece about Fortunate Richard leaving a small sum of money in his will to be used only after it had collected interest for 500 years. Franklin, who was 79 years old at the time, wrote back to the Frenchman, thanking him for a great idea and telling him that he had decided to leave a bequest to his native Boston and his adopted Philadelphia of 1,000 pounds to each on the condition that it be placed in a fund that would gather interest over a period of 200 years.

"...I wish to be useful even after my Death, if possible, in forming and advancing other young men that may be serviceable to their Country both in Boston and Philadelphia. To this end I devote Two thousand Pounds Sterling, which I give, one thousand thereof to the Inhabitants of the Town of Boston in Massachusetts, and the other thousand to the Inhabitants of the City of Philadelphia, in Trust and for the Uses, Interests and Purposes herinafter mentioned and declared....."



Franklin's plan was to lend money to young apprentices. The fund would charge a certain interest rate to the borrowers, and would earn annual interest when each borrower would pay back principal plus interest each year. In addition, Franklin had plans for how the money would be used:
"... If this plan is executed and succeeds as projected without interruption for one hundred Years, the Sum will be one hundred and thirty-one thousand Pounds of which I would have the Managers of the Donation to the Inhabitants of the Town of Boston, then lay out at their discretion one hundred thousand Pounds in Public Works......The remaining thirty-one thousand Pounds, I would have continued to be let out on Interest in the manner above directed for another hundred Years.....At the end of this second term if no unfortunate accident has prevented the operation the sum will be Four Millions and Sixty-one Thousand Pounds.... of which I leave one million sixty-one thousand pounds to the disposition of the inhabitants of the town..., and three millions to the disposition of the government of the State, not presuming to carry my views farther."

So Ben Franklin planned on 1000 pounds being invested for 100 years, compounding yearly, and growing to a balance of 131000 pounds after the first hundred years. The borrowers are paying back money each year (so that the fund can earn interest), but the lump sum formula is still appropriate to use here (Hint: think about how often Ben put money into the account and think about how this relates to the choice of the formula).

After the first hundred years, Franklin planned that reinvesting 31,000 pounds of the 131,000 pounds (the remaining 100,000 pounds would go to each town for "public works") for the second hundred years would result in 4,061,000 pounds.
The Actual First Hundred Years Even though the fund charged borrowers the interest rate Franklin had planned on charging, it was not always possible to find as many borrowers as Franklin had planned and there were other problems as well since some of the borrowers did not pay back their loans. Note: The change to dollars occurred historically before the end of the first hundred years.

In January 1894, at the end of 100 years from the inception of the Franklin gift, because of these problems, the Boston fund had grown from $4444.44 dollars (the equivalent of $1000 pounds) to $391,000 dollars. (Note that this is less than the $582,221.64 (the equivalent of 131,000 pounds) that Franklin had imagined.)

At the end of 100 years the Philly fund had grown from $4444.44 dollars to only $172,350 dollars.

The Actual Second Hundred Years As per Ben Franklin's wishes, a portion of the earnings from the first hundred years went back into the fund to be loaned out, while the remainder was given to the cities.

In Boston, $100,000 was reinvested at the end of the first hundred years. By lending money to borrowers and charging interest, the fund grew to 5 million dollars ($5,000,000) at the end of the second hundred years.

In Philly, $39,274 was reinvested at the end of the first hundred years. By lending money to borrowers and charging interest, the fund grew to $2,256,952.05 by the end of the second hundred years.

As I mentioned previously, this all really happened (and all of the numbers are the actual numbers). So, at the end of the second hundred years, Boston and Philly had to decide what to do with their respective earnings. Given Ben Franklin's goals and wishes, what would you do with these funds for the cities of Philadelphia and Boston? Think about this in preparation for lab. (In lab you will relate your answer to his goals and wishes.)