The Franklin Technical Institute of Boston owes its existence in
part to a codicil in
Benjamin Franklin's will
(**skim through the codicil by clicking on the underlined link
from the web page**).
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 since 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."

**Make sure you answer all the questions since your lab grade
today will be based on the depth, clarity and correctness of
your responses.
NAME____________________________________________________________
**

Under the apple, under Math 1010 Apps, release on Microsoft Excel. Under File, release on Open, look in the public folder and then click on benf.xls and Open it. You will see a chart that is partly filled in.

=1000*(1+ben1)^100

and then hit return. You will see "#NAME?" since excel doesn't know what ben1 means. We'll define it.

Set cell: should already read C2

Type 131000 in the To value: slot

Type D2 in the By changing cell: slot

Goal Seek will find a solution, so then click on OK. Notice that the interest rate solution is in box D2.

2. Franklin planned that reinvesting 31000 pounds for the second
hundred years would result in 4061000 pounds. If
31000 pounds were invested for 100 years, which interest
rate compounding yearly would give a balance of
4061000 pounds? Answer this in your excel sheet in boxes
C3 and D3 using a similar
process to the one described
above. Think about what your new lump sum formula will be.
**Be sure to use a different
name for the rate. For example,
you could use ben2. In addition, be careful that you insert/name
into the correct box (D3), and that you use goal seek on the
correct box (C3). Once I have checked your work, save your
Excel file and then fill in the second row of the tables.**

4. Assume that Philadelphia had also reinvested
$100,000 at the end of the first hundred years
(I haven't been able to find the actual amount that was reinvested
by Philadelphia). In real-life, the fund grew
to $2256952.05. What average earned interest rate was responsible for
this Philadelphia growth?
Answer this in your excel sheet in boxes
C5 and D5.
**Note that a small difference in the average earned
interest rate resulted in a
substantial difference in the fund's earned income!
Fill in row 4 of the tables. Wait to answer questions 4 and
5 until the end of lab or outside of class.
**

For the first table, in Column C, you should put the formula that you used and in Column D, you should put the names that you defined.

For example, C2 should read

=1000*(1+benone)^100

and D2 should read ben1. To remind yourself of the formulas that you used, click on the corresponding box in Excel, and look at the top next to the equal sign (under view, release on Formula Bar if you do not see this already).

A | B | C | D | |

1 | Info | Time | Money Formula |
Defined Rate
Names |

2 | Ben's Plan | 100 years | ||

3 | Ben's Plan | 200 years | ||

4 | Boston | 200 years | ||

5 | Philly | 200 years |

For the second table, you should fill in the numbers that you see
in Excel. Be sure to write down whether the money is in dollars
or pounds. Turn the interest rates into percentages, but don't round them.

A | B | C | D | |

1 | Info | Time | Money in Pounds or Dollars |
Average Earned Interest Rate
as a Percentage - don't round |

2 | Ben's Plan | 100 years | ||

3 | Ben's Plan | 200 years | ||

4 | Boston | 200 years | ||

5 | Philly | 200 years |

- Write down the lump sum formula, filling in for the variables
that we already know and highlighting the unknown variable.
(No need for complete sentences for this question).

- How does the fund earn the interest that is compounded annually?

- Why is the lump sum formula appropriate to use here - if
the borrowers are paying back money each year, shouldn't we
use the periodic payment formula?

- After 200 years, Boston and Philly ended up with a lot of money using
Ben's loan method, but they ended up with a lot less money than he had
planned (note the difference between pounds and dollars at the time).
Notice that D2 says "Average Rate". Explain in your own words
why this isn't the actual lent interest rate of approximately 5% that
was charged to the lenders.
(Hint - think about the lending process, the problems that occurred
and how this would affect the average earned rate that the fund yielded).

**Worth More**What would you do with these funds for the cities of Philadelphia and Boston? Think about this question carefully, especially in relationship to Ben Franklin's goals, and then answer the question here.