In
order to help get you started, this Sample Ben Word document contains the shell of the paper
along with the general lump sum formula, the lump sum formula for the Plan for
the First Hundred Years, the Excel chart, and a sample section on the Plan for
the Second Hundred Years. You
will change this sample so that it is in your own words in order to reflect
your own writing style. ÒÉÓ indicates
additional writing. Dr. Sarah
Introduction
É
Plan for the First Hundred Years and the Excel Chart
É
The
general lump sum formula is a mathematical equation that is used to solve for
the total amount of money that will be in an account after depositing a certain
amount of money all at once and leaving it to earn interest for a certain
number of years. Since Ben
FranklinÕs codicil designated that the interest would compound annually, in
this case, the general lump sum formula states that
savings = principal (1 + rate)^{years}^{}
where principal
is the amount of money that we deposit as a lump sum.
É
131000 = 1000 (1+ rate)^{100}
É

A 
B 
C 
D 
1 
Info 
Time 
Money 
Average Rate 
2 
Ben's Plan 
100 years 
131000 
0.0499599 
3 
Ben's Plan 
200 years 
4061000 
0.0499599 
4 
Boston 
100 years 
391000 
0.045787863 
5 
Philly 
100 years 
172350 
0.037255968 
6 
Boston 
200 years 
5000000 
0.039895503 
7 
Philly 
200 years 
2256952 
0.041343887 
Table 1: Excel Chart
É
Plan for the Second Hundred Years
Ben Franklin
proposed that the savings be divided up at the end of the first hundred
years. His codicil stipulated that
each city should use approximately threequarters of their earnings for
projects that would benefit the public.
In a plan that was similar to his plan for the first hundred years, the
remaining funds, approximately 31,000 pounds, were to be used for the next
hundred years in order to loan money to young married apprentices
in order to help them start their own businesses. While Ben Franklin calculated that the savings in each city
at the end of the second hundred years would total 4,061,000 pounds, his
codicil did not include the planned interest rate for the loans. Yet, the codicil did specify the lump
sum principal (31,000 pounds), the number of years that the money would earn
interest via the loan process (100 years) and the total intended savings
(4,061,000), and so we can set up the lump sum formula with these numbers
plugged in:
4061000 = 31000 (1+ rate)^{100}
We
used Excel to solve for the unknown rate in the formula. In row 3 of the excel chart in Table 1,
we see that a lent rate of 4.99599% in D3 was planned for the growth of 31,000
pounds to the earnings of 4,061,000 pounds in C3. At the end of the second hundred years, Ben Franklin
stipulated that these earnings should be divided between the city and state in
both Boston and Philadelphia. Each
state would receive threequarters of the money, or approximately 3,000,000
pounds, while each city would receive the remaining onequarter, approximately
1,061,000 pounds. He thought that
the government should then decide what to do with these funds: Ònot presuming
to carry my views farther.Ó
Actual First Hundred Years in Boston
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Actual First Hundred Years in Philadelphia
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Difference Between the Lent Rate and Earned Rate
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Actual Second Hundred Years in Boston
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Actual Second Hundred Years in Philadelphia
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Disposition of the Funds in Boston
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Disposition of the Funds in Philadelphia
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Comparison of Boston and Philadelphia's Earnings and Fund
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Disposition in Relationship to the Goals Listed in the Codicil
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Conclusion
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