"...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....."

1. Take out class notes and write down both sides of your lump sum formula.

2.
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
$

_____________________________________________ To solve for the average earned rate of the fund (the answer is not 5% because of the problems that the fund faced) we could guess what average earned rate compounding yearly would give a balance of

=4444.44*(1+ben1)^100

and then hit return. You will see "#NAME?"

3. At the end of 100 years the Philly fund had grown from
$** 4444.44** dollars to only $

_____________________________________________ Solve for the average earned interest rate responsible for this Philly growth in your Excel sheet in boxes C3 and D3.

=4444.44*(1+ben2)^100

and then hit return. You will see "#NAME?"

A | B | C | D | |

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

2 | Boston | 100 years | =4444.44*(1+ben1)^100 | ben1 |

3 | Philly | 100 years | =4444.44*(1+ben2)^100 | ben2 |

4 | Boston | 200 years | ||

5 | Philly | 200 years |

A | B | C | D | |

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

2 | Boston | 100 years | 391000 dollars | 4.5787863% |

3 | Philly | 100 years | 172,350 dollars | 3.7255968% |

4 | Boston | 200 years | dollars | |

5 | Philly | 200 years | dollars |

**
Make sure that you understand the
Excel commands and the related lump sum formulas
before you move on. **
Notice that the Excel process is the same in both cases:
We set up the lump sum formula in the C box, define the name in the D
box, and then use Goal Seek back on the C box.

4. In Boston, $

_____________________________________________ Solve for the average earned rate of the fund (the answer is not 5% since the fund faced similar problems as were faced during the first hundred years) in your Excel sheet in boxes C4 and D4, and then fill in the relevant row of both tables above. Be sure to use a different name for the rate. For example, you could use ben3. In addition,

5. In Philly, $** 39,274**
was reinvested at the end of the first hundred
years. By lending money to borrowers at 5% interest,
the fund grew
to $

_____________________________________________ Solve for the average earned rate of the fund in your Excel sheet in boxes C5 and D5, and then fill in the relevant row of both tables above.

6. We'll see what happened to the these earnings in Ben Franklin Part 2.

7. If the borrowers are paying back money each year (so that the fund can earn interest), why is the lump sum formula appropriate to use here? Think about how often Ben put money into the account and relate this to the choice of the formula. Also address why the interest coming back every year is already accounted for in the lump sum formula by relating your answer to our discussion of the philosophy of the derivation of the formula in class.

8. 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. 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? Relate your answer to the definition of average, the lending process, the problems that occurred, and how these would affect the average earned rate that the fund yielded.

9. 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? Relate your answer to his goals and wishes from the homework reading.